1. A and B completed a work together in 5 days. had A worked at twice the speed and B at half the speed, it would have taken them four days to complete the job. How much time would it take for A alone to do the work?
a) 10 days
b) 20 days
c) 25 days
d) 24 days
Discussion
Explanation: Assume work to be done 100%.
First case,
A + B = $$\frac{{100}}{5}$$ = 20% work done per day -------- (1)
Second case,
2A + $$\frac{{\text{B}}}{2}$$ = $$\frac{{100}}{4}$$ = 25% work done per day ------ (2)
On solving equation (1) and (2), we get
A = 10 days
2. The charges per hour of internet surfing is increased by 25% then find the percentage decrease in the time period of surfing user (a net savy) who can afford only 10% increase in expenditure:
a) 22%
b) 12%
c) 15%
d) 9.09%
Discussion
Explanation: Time × Rate = total charges
100 × 100 = 10000
X × 125 = 110 [25% increase in rate, user can afford only 10% increase]
X = $$\frac{{110}}{{125}} \times 100$$ = 88%
Thus, decrease in time = 12%
3. A group of workers was put on a job. From second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in 55% of the time. How many workers were there in the group?
a) 15
b) 14
c) 12
d) 10
Discussion
Explanation: Let initially X number of workers
Using work equivalence method,
X + (X - 1) + (X - 2) + . . . . . + 1 = X × 55% of X
$$\frac{{{\text{X}} \times \left( {{\text{X}} + 1} \right)}}{2} = \frac{{5{\text{X}}}}{{100}}$$
[series is in AP. Sum of AP = {No. of terms (first term + last term)/2}]
X = 10 workers.
4. X takes 4 days to complete one-third of a job. Y takes 3 days to complete one-sixth of the job and Z takes 5 days to complete half the job. If all of them work together for 3 days and X and Z quit, how long will it take for Y to complete the remaining work done.
a) 6 days
b) 8.1 days
c) 5.1 days
d) 7 days
Discussion
Explanation: X completes $$\frac{1}{3}$$ rd in 4 days = 33.33% job in 4 days
X one day work = 8.33%
Y one day work = 5.55% [As he complete $$\frac{1}{6}$$ job = 16.66% job in 3 days]
Z one day work = 10%
Work done in 3 days by X, Y and Z
= 25 + 16.66 + 30 = 71.66%
Remaining work will be done by Y,
$$\frac{{28.33}}{{5.55}}$$ = 5.1 days
5. A and B can compete a piece of work in 18 days. They worked together for 12 days and then A left. B alone finished the work in 15 days. If Rs. 1500 be paid for the work then A's share is:
a) Rs. 750
b) Rs. 800
c) Rs. 900
d) Rs. 600
Discussion
Explanation: A and B can complete the work in 18 days, work rate = $$\frac{{100}}{{18}}$$ = 5.55% per day
They together can complete the work in 12 days = 5.55 × 12 = 66.60%
Now, A leaves and B takes another 15 days to complete the whole work, Work rate of B = $$\frac{{33.30}}{{15}}$$ = 2.22% per day
B work for (12 + 15) = 27 days
So, Work done by B in 27 days = 2.22 × 27 ≈ 60% And So 40% work is done by A. so there share should be 60% and 40% ratio.
A's share = 40% of 1500 = Rs. 600
6. To complete a piece of work A and B take 8 days, B and C 12 days. A, B and C take 6 days. A and C will take :
a) 7 Days
b) 8 Days
c) 7.5 Days
d) 8.5 Days
Discussion
Explanation: Given (A+B)'s one day's work = $$\frac{1}{8}$$
(B + C)'s one day's work = $$\frac{1}{{12}}$$
(A + B + C) 's 1 day's work = $$\frac{1}{6}$$
Work done by A, alone= (A + B + C) 's 1 day's work - (B + C)'s one day's work
$$ = \frac{1}{6} - \frac{1}{{12}} = \frac{{2 - 1}}{{12}} = \frac{1}{{12}}$$
Work done by C, alone = (A + B + C) 's 1 day's work - (A + B)'s one day’s work
$$ = \frac{1}{6} - \frac{1}{8} = \frac{{4 - 3}}{{24}} = \frac{1}{{24}}$$
⇒ (A + C)’s one day’s work
$$\eqalign{ & = \frac{1}{{12}} + \frac{1}{{24}} \cr & = \frac{{2 + 1}}{{24}} \cr & = \frac{3}{{24}} = \frac{1}{8} \cr} $$
⇒ (A + C) will take 8 days to complete the work together
7. 42 women can do a piece of work in 18 days, How many women would be required do the same work in 21 days.
a) 35
b) 36
c) 37
d) 38
Discussion
Explanation: Let K be the number of women required to finish the work in 21 days.
Now, using Work Equivalence Method:
42 × 18 = K × 21
K = 36.
Number of women required = 36
8. Working together B and C take 50% more number of days than A, B and C together take and A and B working together, take $$\frac{8}{3}$$ more number of days than A, B and C take together. If A, B and C all have worked together till the completion of the work and B has received Rs. 120 out of total earnings of Rs. 450, then in how many days did A, B and C together complete the whole work?
a) 2 days
b) 4 days
c) 6 days
d) 8 days
Discussion
Explanation: Ratio of efficiencies of A, B and C,
= 5x : 4x : 6x
Number of days required by A and B = $$\frac{{100}}{{9{\text{x}}}}$$ ------ (1)
Number of days required by A, B and C = $$\frac{{100}}{{15{\text{x}}}}$$ ------ (2)
$$\eqalign{ & \frac{{100}}{{9{\text{x}}}} - \frac{{100}}{{15{\text{x}}}} = \frac{8}{3} \cr & \Rightarrow {\text{x}} = \frac{5}{3} \cr} $$
Number of days required by A, B and C
= $$\frac{{100}}{{15{\text{x}}}}$$
= $$\frac{{100}}{{15 \times \frac{5}{3}}}$$
= 4 days
9. A is thrice good a workman as B and therefore is able to finish a job in 40 days less than B. Working together they can do it in :
a) 15 days
b) 16 days
c) 18 days
d) 20 days
Discussion
Explanation: A is thrice good workman as B means,
A = 3B
Let B can finish work in X days, then A will finish same work in (X - 40) days alone
BX = 3B × (X - 40)
X = 60 days
B can finish work in 60 days, then A can finish the work in 20 days.
One day work of B = $$\frac{1}{{60}}$$
One day work of A = $$\frac{1}{{20}}$$
One day work of (A+B) =
$$\frac{1}{{60}} + \frac{1}{{20}} \Rightarrow \frac{{1 + 3}}{{60}} \Rightarrow \frac{1}{{15}}$$
So, they can finish work together in 15 days
10. Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 20hr. If all pipes are opened simultaneously, then the cistern will be filled in:
a) 8 hr
b) 7.5 hr
c) 8.5 hr
d) 10 hr
Discussion
Explanation: Work done by all the tanks working together in 1 hour,
$$ \Rightarrow \frac{1}{{10}} + \frac{1}{{12}} - \frac{1}{{20}} = \frac{2}{{15}}$$
Hence, tank will be filled in $$\frac{{15}}{2}$$ = 7.5 hour.
11. A group of men decided to do a job in 4 days. But since 20 men dropped out every day, the job completed at the end of the 7th day. How many men were there at the beginning?
a) 240
b) 280
c) 140
d) 150
Discussion
Explanation: Let X be the initial number of men -:
4X = X + (X - 20) + (X - 40) + (X - 60) + (X - 80) + (X - 100) + (X - 120)
⇒ 4X = 7X - 420
⇒ 3X = 420
⇒ X = $$\frac{{420}}{3}$$
⇒ X = 140 men
12. Two typist of varying skills can do a job in 6 minutes if they work together. If the first typist typed alone for 4 minutes and then the second typist typed alone for 6 minutes, they would be left with $$\frac{1}{5}$$ of the whole work. How many minutes would it take the slower typist to complete the typing job working alone ?
a) 10 minutes
b) 15 minutes
c) 12 minutes
d) 17 minutes
Discussion
Explanation: Working efficiency of both typist together,
= $$\frac{{100}}{6}$$ = 16.66% per minute
Now, let work efficiency of first typist be x and then second typist will be (16.66 - x)
First typist typed alone for 4 minutes and second typed alone for 6 minutes and they left with $$\frac{1}{5}$$ (i.e 20%) of job, means they have completed 80% job
First Typist typed in 4 minute + Second typed in 6 minutes = 80%
4 × x + 6 × (16.66 - x) = 80%
4x + 100% - 6x = 80%
x = 10%
First Typist typed 10% per minutes. Then second typed (16.66 - 10) = 6.66% per minute
Then, Second typist complete the whole job in $$\frac{{100}}{{6.66}}$$ = 15.01 = 15 minutes.
13. Two persons having different productivity of labour, working together can reap a field in 2 days. If one-third of the field was reaped by the first man and rest by the other one working alternatively took 4 days. How long did it take for the faster person to reap the whole field working alone?
a) 3
b) 6
c) 8
d) 12
Discussion
Explanation: Total efficiency of two persons = 50% [As they complete work in 2 days]
First Person completes work = $$\frac{1}{3}$$ = 33.33% [In 2 days]
Rest work will be completed by Second man = $$\frac{2}{3}$$ = 66.66% [In 2 days]
So, efficiency of second person is greater.
Efficiency of second person = $$\frac{{66.66}}{2}$$ = 33.33% per day
Then, Second person will complete whole work in,
= $$\frac{{100}}{{33.33}}$$ = 3 days.
14. If m men can do a work in r days, then the number of days taken by (m + n) men to do it is :
a) $$\frac{{{\text{m}} + {\text{n}}}}{{{\text{mn}}}}$$
b) $$\frac{{{\text{r}}\left( {{\text{m}} + {\text{n}}} \right)}}{{{\text{mn}}}}$$
c) $$\frac{{{\text{m}} + {\text{n}}}}{{{\text{mr}}}}$$
d) $$\frac{{{\text{mr}}}}{{{\text{m}} + {\text{n}}}}$$
Discussion
Explanation: M1 × D1 = M2 × D2
mr = (m +n) × D2
D2 = $$\frac{{{\text{mr}}}}{{{\text{m}} + {\text{n}}}}$$
15. If 10 persons can do a job in 20 days, then 20 person with twice the efficiency can do the same job in:
a) 5 days
b) 40 days
c) 10 days
d) 20 days
Discussion
Explanation: By work equivalence method,
man × days × work = MAN × DAYS × WORK
10 × 20 × 1 = 20 × 2 × x
→ x = 5 days
16. If 2 men or 3 women or 4 boys can do a piece of work in 52 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in:
a) 48 days
b) 36 days
c) 45 days
d) 50 days
Discussion
Explanation: Work done by 2 men = 3 women = 4 boys
1 man = 2 boys
1 woman = $$\frac{4}{3}$$ boys
Boys × days = 4 × 52 boys × days
1 man + 1 women + 1 boys,
$$ = 2 + \frac{4}{3} + 1$$
$$ = \frac{{13}}{3}$$ boys
Using work equivalent method,
boys × day = BOYS × DAYS
$$4 \times 52 = \frac{{13}}{3} \times {\text{x}}\,{\text{(let)}}$$
x = 48 days
17. Two men and women are entrusted with a task. The second man needs three hours more to cope up with the job than the second man and the woman would need working together. The first man, working alone, would need as much time as second man and the woman working together. The first man working alone, would spend eight hours less than the double period of the time second man would spend working alone. How much time would the two men and the women need to complete the task if they all asked together?
a) 2 hours
b) 1 hour
c) 3 hours
d) 4 hours
Discussion
Explanation: Difference in times required by the first man (A) and second man (B) = 3 hours. Also, if ta and tb are the respective times, then
tb - ta = 3 . . . . . . . . . ..(1)
Also, B alone be take = (ta + 3) h
2tb - ta = 8
2 × (ta + 3) - ta = 8 [Using equation (1)]
ta = 2 hours.
Now B and woman together take 2 hours and A also take 2 hours, so time required will be half when all 3 work together. So in 1 hour work would be completed.
18. If 3 men or 4 women can plough a field in 43 days, how long will 7 men and 5 women take to plough it?
a) 10 days
b) 11 days
c) 9 days
d) 12 days
Discussion
Explanation: 3 men or 4 women can plough the field in 43 days
3 men = 4 women
1 man = $$\frac{4}{3}$$ women
7 man = $$\frac{{28}}{3}$$ women
7 men and 5 women = $$5 + \frac{{28}}{3}$$ = $$\frac{{43}}{3}$$ women
4 women can plough field in 43 days
So, 1 women can plough in = 43 × 4 days
$$\frac{{43}}{3}$$ women can plough = $$\frac{{43 \times 4 \times 3}}{{43}}$$ = 12 days
19. Raj can do a piece of work in 20 days. He started the work and left after some days, when 25% work was done. After it Abhijit joined and completed it working for 10 days. In how many days Raj and Abhijit can do the complete work, working together?
a) 8
b) 6
c) 10
d) 12
Discussion
Explanation: Efficiency of Raj = $$\frac{{100}}{{20}}$$ = 5%
Work completed by Raj = 25%
Rest work = 75%
Efficiency of Abhijit = $$\frac{{75}}{{10}}$$ = 7.5%
Combined efficiency = 5 + 7.5 = 12.5%
They will complete the whole work by working together in,
= $$\frac{{100}}{{12.5}}$$ = 8 days
20. If one pipe A can fill a tank in 20 minutes, then 5 pipes, each of 20% efficiency of A, can fill the tank in:
a) 80 min
b) 100 min
c) 20 min
d) 25 min
Discussion
Explanation: Efficiency of pipe A,
$$\frac{{100}}{{20}}$$ = 5%
20% of efficiency of A = 1%
Then, efficiency of 5 such pipes = 5%.
Time taken to fill the tank = $$\frac{{100}}{5}$$ = 20 min.
21. A can finish a work in 18 days and B can do the same work in half the time take by A. Then, working together, what part of the same work they can finish in a day ?
a) $$\frac{1}{6}$$
b) $$\frac{1}{9}$$
c) $$\frac{2}{5}$$
d) $$\frac{2}{7}$$
Discussion
Explanation:
$$\eqalign{ & {\text{A's 1 day's work}} = \frac{1}{{18}} \cr & {\text{B's 1 day's work}} = \frac{1}{9} \cr & \left( {{\text{A}} + {\text{B}}} \right)'{\text{s 1 day's work}} \cr & = \left( {\frac{1}{{18}} + \frac{1}{9}} \right) \cr & = \frac{1}{6} \cr} $$
22. A can knit a pair of socks in 3 days. B can knit the same pair of socks in 9 days. If they are knitting together, then in how many days will they knit two pairs of socks ?
a) 3 days
b) 4 days
c) $${\text{4}}\frac{1}{2}$$ days
d) 5 days
Discussion
Explanation: Number of pairs knit by A and B together in 1 day
$$\eqalign{ & = \left( {\frac{1}{3} + \frac{1}{9}} \right) \cr & = \frac{4}{9}{\text{ }} \cr} $$
Required number of days,
$$\eqalign{ & = \left( {2 \div \frac{4}{9}} \right) \cr & = \left( {2 \times \frac{9}{4}} \right) \cr & = \frac{9}{2} \cr & = 4\frac{1}{2} \text{ days} \cr} $$
23. P can complete $$\frac{1}{4}$$ of a work in 10 days, Q can complete 40% of the same work in 145 days. R, complete $$\frac{1}{3}$$ of the work in 13 days and S, $$\frac{1}{6}$$ of the work in 7 days. Who will be able complete the work first ?
a) P
b) Q
c) R
d) S
Discussion
Explanation: P completes $$\frac{1}{4}$$ of work in 10 days
P completes full of work in
$$\eqalign{ & = \frac{{10}}{1} \times 4 \cr & = 40{\text{ days}} \cr} $$
Q completes 40% of work in 145 days
Q completes full 100% of work in
$$\eqalign{ & = \frac{{145}}{{40}} \times 100 \cr & = 362.5{\text{ days}} \cr} $$
R completes $$\frac{1}{3}$$ of work in 13 days
R completes full of work in
$$\eqalign{ & = \frac{{13}}{1} \times 3 \cr & = 39{\text{ days}} \cr} $$
S completes $$\frac{1}{6}$$ of work in 7 days
S completes full of work in
$$\eqalign{ & = \frac{7}{1} \times 6 \cr & = 42{\text{ days}} \cr} $$
We can see R completes the work first
24. George takes 8 hours to copy a 50-page manuscript while Sonia can copy the same manuscript in 6 hours. How many hours would it take them to copy a 100-page manuscript, if they work together ?
a) $$6\frac{6}{7}\,\,{\text{hours}}$$
b) $${\text{9 hours}}$$
c) $$9\frac{5}{7}\,\,{\text{hours}}$$
d) $${\text{14 hours}}$$
Discussion
Explanation: Number of pages typed by Gorge in 1 hour
$$\eqalign{ & = \frac{{50}}{8} \cr & = \frac{{25}}{4} \cr} $$
Number of pages typed by Sonia in 1 hour
$$\eqalign{ & = \frac{{50}}{6} \cr & = \frac{{25}}{3} \cr} $$
Number of pages typed by Gorge and Sonia together in 1 hour
$$\eqalign{ & = \left( {\frac{{25}}{4} + \frac{{25}}{3}} \right) \cr & = \left( {\frac{{75 + 100}}{{12}}} \right) \cr & = \frac{{175}}{{12}} \cr & {\text{Required time}} \cr & = \left( {100 \div \frac{{175}}{{12}}} \right){\text{hours}} \cr & = \left( {\frac{{100 \times 12}}{{175}}} \right){\text{ hours}} \cr & = \frac{{48}}{7}{\text{ hours}} \cr & = 6\frac{6}{7}{\text{ hours}} \cr} $$
25. A and B together complete a piece of work in T days. If A alone completes the work in T + 3 days and B alone completes the piece of work in T + 12 days, what is T ?:
a) 3 days
b) 9 days
c) 12 days
d) None of these
Discussion
Explanation:
$$\eqalign{ & {\text{A's 1 day's work}} \cr & = \frac{1}{{{\text{T}} + 3}} \cr & {\text{B's 1 day's work}} \cr & = \frac{1}{{{\text{T}} + 12}} \cr & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} = \frac{1}{{\text{T}}} \cr & \therefore \frac{1}{{{\text{T}} + 3}} + \frac{1}{{{\text{T}} + 12}} = \frac{1}{{\text{T}}} \cr & \Rightarrow \frac{{2{\text{T}} + 15}}{{\left( {{\text{T}} + 3} \right)\left( {{\text{T}} + 12} \right)}} = \frac{1}{{\text{T}}} \cr & \Rightarrow 2{{\text{T}}^2} + 15{\text{T}} = {{\text{T}}^2} + 15{\text{T}} + 36 \cr & {{\text{T}}^2} = 36 \cr & {\text{T}} = 6 \cr} $$
26. X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?
a) $$13\frac{1}{3}$$ days
b) 15 days
c) 20 days
d) 26 days
Discussion
Explanation: Work done by X in 8 days = $$ {\frac{1}{{40}} \times 8} $$ = $$\frac{1}{5}$$
Remaining work = $$ {1 - \frac{1}{5}} $$ = $$\frac{4}{5}$$
Now, $$\frac{4}{5}$$ work is done by Y in 16 days
Whole work will be done by Y in = $$ {16 \times \frac{5}{4}} $$ = 20 days
X's 1 day's work = $$\frac{1}{{40}}$$
Y's 1 day's work = $$\frac{1}{{20}}$$
(X + Y)'s 1 day's work
$$\eqalign{ & = {\frac{1}{{40}} + \frac{1}{{20}}} \cr & = \frac{3}{{40}} \cr} $$
Hence, X and Y will together complete the work in
$$\eqalign{ & = {\frac{{{\text{40}}}}{{\text{3}}}} \cr & {\text{ = 13}}\frac{{\text{1}}}{{\text{3}}}\,\,{\text{days}} \cr} $$
27. A and B can do a job together in 7 days. A is $$1\frac{3}{4}$$ times as efficient as B. The same job can be done by A alone in :
a) $$9\frac{1}{3}$$ days
b) 11 days
c) $$12\frac{1}{4}$$ days
d) $$16\frac{1}{3}$$ days
Discussion
Explanation:
$$\eqalign{ & \left( {{\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}}} \right){\text{:}}\left( {{\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}}} \right) \cr & = \frac{7}{4}:1 = 7:4 \cr & {\text{Let}}\,{\text{A's}}\,{\text{and}}\,{\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}}\,{\text{be}} \cr & 7x\,{\text{and}}\,4x\,{\text{respectively}} \cr & {\text{Then}},\,7x + 4x = \frac{1}{7} \cr & 11x = \frac{1}{7} \cr & x = \frac{1}{{77}} \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{77}} \times {\text{7}}} = \frac{1}{{11}} \cr} $$
So, A will do the work in 11 days
28. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
a) 30 days
b) 40 days
c) 60 days
d) 70 days
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = x\,{\text{and}} \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = y \cr & {\text{Then}},\,x + y = \frac{1}{{30}} \cr & 16x + 44y = 1 \cr & {\text{Solving}}\,{\text{these}}\,{\text{two}}\,{\text{equations,}} \cr & x = \frac{1}{{60}}\,{\text{and}}\,y = \frac{1}{{60}} \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{60}} \cr & {\text{Hence,}}\,{\text{B}}\,{\text{alone}}\,{\text{shall}}\,{\text{finish}}\,{\text{the}}\,{\text{whole}}\,{\text{work}}\,{\text{in}}\,{\text{60}}\,{\text{days}} \cr} $$
29. A can finish a piece of work in 18 days and B can do the same work in half of the time taken by A. Then working together what part of the same work they can finish in a day ?
a) $$\frac{1}{6}$$
b) $$\frac{2}{5}$$
c) $$\frac{1}{9}$$
d) $$\frac{2}{7}$$
Discussion
Explanation: A's 1 day work = $$\frac{1}{{18}}$$
B's 1 day work = $$\frac{1}{9}$$ [because B take half time than A]
(A + B)'s one day work
$$\eqalign{ & = {\frac{1}{{18}} + \frac{1}{9}} \cr & = {\frac{{1 + 2}}{{18}}} \cr & = \frac{1}{6} \cr} $$
30. A and B can do a piece of work in 72 days, B and C can do it in 120 days and A and C can do it in 90 days. In how many days all three together can do the work ?
a) 80 days
b) 100 days
c) 60 days
d) 150 days
Discussion
Explanation: In these type of questions, always take total work as L.C.M. of number of days.
Here L.C.M. of Total Work = 360
One day work of A + B = $$\frac{{360}}{{72}}$$ = 5 unit/day
One day work of B + C = $$\frac{{360}}{{120}}$$ = 3 unit/day
One day work of C + A = $$\frac{{360}}{{90}}$$ = 4 unit/day
Total units/day = 5 + 3 + 4 = 12
(Here , 12 unit represents twice of the work done by A, B and C. So we will divide it by 2)
Work done by (A + B + C) per day = $$\frac{{12}}{2}$$ = 6 units/day
Total time taken by (A + B + C)
$$\eqalign{ & = \frac{{360}}{6} \cr & = 60{\text{ days}} \cr} $$
31. A can do a piece of work in 20 days and B in 40 days. If they work together for 5 days, then the fraction of the work that is left is ?
a) $$\frac{5}{8}$$
b) $$\frac{8}{{15}}$$
c) $$\frac{7}{{15}}$$
d) $$\frac{1}{{10}}$$
Discussion
Explanation: L.C.M of total work = 40
One day work of A = $$\frac{{40}}{{20}}$$ = 2 unit/day
One day work of B = $$\frac{{40}}{{40}}$$ = 1 unit/day
(A + B)'s one day work is (2 + 1) units
(A + B)'s 5 day work is 3 × 5 = 15 units
Work left = 40 - 15 = 25
Fraction of work left
$$\eqalign{ & = \frac{{{\text{Work left}}}}{{{\text{Total work}}}} \cr & = \frac{{25}}{{40}} \cr & = \frac{5}{8} \cr} $$
32. If there is a reduction in the number of workers in a factory in the ratio 15 : 11 and an increment in their wages in the rate 22 : 25, then the ratio by which the total wages of the workers should be decreased is =
a) 6 : 5
b) 5 : 6
c) 3 : 7
d) 3 : 5
Discussion
Explanation:
| Earlier | : | Now | |
| No.of worker | 15 | : | 11 |
| Wages | 22 | : | 25 |
| Total wages | 330 | 275 | |
| Total wages | 6 | : | 5 |
33. x does $$\frac{1}{4}$$ of a job in 6 days. y completes rest of the job in 12 days. Then x and y could complete the job together in = ?
a) $${\text{9 days}}$$
b) $${\text{8}}\frac{1}{8}{\text{ days}}$$
c) $${\text{9}}\frac{3}{5}{\text{ days}}$$
d) $${\text{7}}\frac{1}{3}{\text{ days}}$$
Discussion
Explanation: x does $$\frac{1}{4}$$ work in 6 days.
x does complete work in 6 × 4 = 24 days
y does complete the $$\frac{3}{4}$$ work in 12 days.
y does complete work in 12 × $$\frac{4}{3}$$ = 16 days
x and y together can complete a work in
$$\eqalign{ & = \frac{{16 \times 24}}{{16 + 24}} \cr & = \frac{{48}}{5} \cr & = 9\frac{3}{5}\,{\text{days}} \cr} $$
34. Reena, Aastha and Shloka can independently complete a piece of work in 6 hours, 4 hours and 12 hours respectively. If they work together, how much time will they take to complete that piece of work ?
a) 2 hours
b) 5 hours
c) 6 hours
d) 8 hours
Discussion
Explanation:
$$\eqalign{ & {\text{Reena's 1 hour's work}} = \frac{1}{6}{\text{ }} \cr & {\text{Aastha's 1 hour's work}} = \frac{1}{4}{\text{ }} \cr & {\text{Shloka's 1 hour's work}} = \frac{1}{{12}}{\text{ }} \cr} $$
( Reena + Aastha + Shloka )'s 1 hour's work
$$\eqalign{ & = \frac{1}{4} + \frac{1}{6}{\text{ + }}\frac{1}{{12}} \cr & {\text{ = }}\frac{6}{{12}} \cr & = \frac{1}{2} \cr} $$
They together take 2 hours to complete the work.
35. Amit and Sumit can plough a field in 4 days. Sumit alone can plough the field in 6 days. In how many days will Amit alone plough the feild ?
a) 10 days
b) 12 days
c) 14 days
d) 15 days
Discussion
Explanation:
$$\eqalign{ & {\text{Amit's 1 day's work }} \cr & = \left( {\frac{1}{4} - \frac{1}{6}} \right) \cr & = \frac{1}{{12}} \cr} $$
Amit alone can plough the field in 12 days.
36. Working efficiencies of P and Q for completing a piece of work are in the ratio 3 : 4. The number of days to be taken by them to complete the work will be in the ratio ?
a) 3 : 2
b) 2 : 3
c) 3 : 4
d) 4 : 3
Discussion
Explanation: Since we know efficiency and time are inversely proportional to each other.
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{P}}:{\text{Q}} \cr & {\text{Efficiency }}3:4 \cr & {\text{Time }}\,\,\,\,\,\,\,\,\,\,{\text{ }}4:3 \cr} $$
37. 5 men can do a piece of work in 6 days while 10 women can do it in 5 days. In how many days can 5 women and 3 men do it ?
a) 4 days
b) 5 days
c) 6 days
d) 8 days
Discussion
Explanation:
$$\eqalign{ & {\text{5M}} \times {\text{6 days}} = {\text{10W}} \times {\text{5 days}} \cr & {\text{3M}} = {\text{5W}} \cr & \frac{{\text{M}}}{{\text{W}}} = \frac{5}{3} \cr & 1{\text{M}}\left( {{\text{work}}} \right) = 5{\text{ units/day}} \cr & {\text{1W}}\left( {{\text{work}}} \right) = 3{\text{ units/day}} \cr & {\text{Total work}} \cr & = \left( {{\text{5M}} \times {\text{6}}} \right) \cr & = {\text{5}} \times {\text{5}} \times {\text{6}} \cr & = {\text{150 units}} \cr & {\text{Required time for }}\left( {{\text{5W}} + {\text{3M}}} \right) \cr & = \frac{{{\text{Total work}}}}{{{\text{Work done/day}}}} \cr & = \frac{{150}}{{\left( {5 \times 3 + 3 \times 5} \right)}} \cr & = \frac{{150}}{{30}} \cr & = 5{\text{ days}} \cr} $$
38. A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With the help of C, they did the job in 4 days only. Then, C alone can do the job in ?
a) $${\text{9}}\frac{1}{5}{\text{ days}}$$
b) $${\text{9}}\frac{2}{5}{\text{ days}}$$
c) $${\text{9}}\frac{3}{5}{\text{ days}}$$
d) $${\text{10 days}}$$
Discussion
Explanation:
$$\eqalign{ & \left( {{\text{A}} + {\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} = \frac{1}{4} \cr & {\text{A's 1 day's work}} = \frac{1}{{16}} \cr & {\text{B's 1 day's work}} = \frac{1}{{12}} \cr & {\text{C's 1 day's work}} \cr & = \frac{1}{4} - \left( {\frac{1}{{16}} + \frac{1}{{12}}} \right) \cr & = \left( {\frac{1}{4} - \frac{7}{{48}}} \right) \cr & = \frac{5}{{48}} \cr & {\text{So, C alone can do the work in }} \cr & = \frac{{48}}{5} \cr & = 9\frac{3}{5}{\text{ days}} \cr} $$
39. A can complete $$\frac{1}{3}$$ of a work in 5 days and B, $$\frac{2}{5}$$ of the work in 10 days. In how many days both A and B together can complete the work ?
a) $${\text{7}}\frac{1}{2}$$
b) $${\text{8}}\frac{4}{5}$$
c) $${\text{9}}\frac{3}{8}$$
d) 10
Discussion
Explanation: Whole work will be done by A in
$$\eqalign{ & = \left( {5 \times 3} \right) \cr & = 15{\text{ days}} \cr} $$
Whole work will be done by B in
$$\eqalign{ & = \left( {10 \times \frac{5}{2}} \right) \cr & = 25{\text{ days}} \cr} $$
$$\eqalign{ & {\text{A's 1 day's work}} = \frac{1}{{15}} \cr & {\text{B's 1 day's work}} = \frac{1}{{25}} \cr & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} \cr & {\text{ = }}\left( {\frac{1}{{15}} + \frac{1}{{25}}} \right) \cr & = \frac{{16}}{{150}} \cr & = \frac{8}{{75}} \cr} $$
A and B together can complete the work in
$$\eqalign{ & = \frac{{75}}{8} \cr & = 9\frac{3}{8}{\text{days}}{\text{.}} \cr} $$
40. If 3 men or 6 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same piece of work ?
a) 4 days
b) 5 days
c) 3 days
d) 2 days
Discussion
Explanation:
$$\eqalign{ & {\text{3m}} \times {\text{16}} = {\text{6w}} \times {\text{16}} \cr} $$
$$\frac{{\text{m}}}{{\text{w}}} = $$ $$\frac{{2 \to {\text{Efficiency of men}}}}{{1 \to {\text{Efficiency of women}}}}$$
$$\eqalign{ & {\text{Total work}} = 3 \times 2 \times 16 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 96{\text{ units}} \cr} $$
$${\text{One day work of}}$$ $$\left( {{\text{12m}} + {\text{8w}}} \right)$$
$$\eqalign{ & = 12 \times 2 + 8 \times 1 \cr & = 32{\text{ units}} \cr} $$
$${\text{Total time taken by}}$$ $$\left( {{\text{12m}} + {\text{8w}}} \right)$$
$$\eqalign{ & = \frac{{96}}{{32}} \cr & = 3{\text{ days}} \cr} $$
41. Janardan completes $$\frac{2}{3}$$ of his work in 10 days. Time he will take to complete of the same $$\frac{3}{5}$$ work, is ?
a) 4 days
b) 8 days
c) 6 days
d) 9 days
Discussion
Explanation: Janardan completes $$\frac{2}{3}$$ of work in 10 days
Janardan completes 1 of work in
$$\eqalign{ & = \frac{{10 \times 3}}{2} \cr & = 15{\text{ days}} \cr} $$
He completes $$\frac{3}{5}$$ of work in
$$\eqalign{ & = 15 \times \frac{3}{5} \cr & = 9{\text{ days}} \cr} $$
42. A can do a piece of work in 12 days while B alone can do it in 15 days. With the help of C they can finish it in 5 days. If they are paid Rs. 960 for the whole work. How much money A gets ?
a) Rs. 480
b) Rs. 240
c) Rs. 320
d) Rs. 400
Discussion
Explanation: (A + B)'s 1 day work
$$\eqalign{ & = \frac{1}{{12}} + \frac{1}{{15}} \cr & = \frac{{5 + 4}}{{60}} \cr & = \frac{9}{{60}} = \frac{3}{{20}} \cr} $$
(A + B + C)'s 1 day work = $$\frac{1}{5}$$
C's 1 day work
$$\eqalign{ & = \frac{1}{5} - \frac{3}{{20}} \cr & = \frac{{4 - 3}}{{20}} \cr & = \frac{1}{{20}} \cr} $$
Ratio of their work
$$\eqalign{ & = \frac{1}{{12}}:\frac{1}{{15}}:\frac{1}{{20}} \cr & = 5:4:3 \cr} $$
$$\eqalign{ & {\text{A's}}\,{\text{share}} = \frac{5}{{12}} \times 960 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}400 \cr} $$
43. Two spinning machines A and B can together produce 300000 metres of cloth in 10 hours. If machine B alone can produce the same amount of cloth in 15 hours. Then how much cloth can machine A produce alone in 10 hours ?
a) 50000 metres
b) 100000 metres
c) 150000 metres
d) 200000 metres
Discussion
Explanation: Length of cloth produced by A and B in 10 hours
$$ = 300000{\text{ metres}}$$
Length of cloth produced by B in 10 hours
$$\eqalign{ & = \left( {\frac{{300000}}{{15}} \times 10} \right) \cr & = 200000{\text{ metres}} \cr} $$
Length of cloth produced by A in 10 hours
$$\eqalign{ & = \left( {300000 - 200000} \right) \cr & = 100000{\text{ metres}} \cr} $$
44. X, Y and Z complete a work in 6 days. X or Y alone can do the same work in 16 days. In how many days Z alone can finish the same work ?
a) 12
b) 16
c) 24
d) 36
Discussion
Explanation: (X + Y)'s 1 day's work
$$\eqalign{ & = \left( {\frac{1}{{16}} + \frac{1}{{16}}} \right) \cr & = \frac{2}{{16}} \cr & = \frac{1}{8} \cr} $$
Z's 1 day's work =
(X + Y + Z)'s 1 day's work - (X + Y)'s 1 day's work
$$\eqalign{ & = \frac{1}{6} - \frac{1}{8} \cr & = \frac{1}{{24}} \cr} $$
Z alone can finish the work in 24 days.
45. In two days A, B and C together can finish $$\frac{1}{2}$$ of a work and in another 2 days B and C together can finish $$\frac{3}{{10}}$$ part of the work. Then A alone can complete the whole work in ?
a) 15 days
b) 10 days
c) 12 days
d) 14 days
Discussion
Explanation:
$$\eqalign{ & \frac{3}{{10}}\left( {{\text{B}} + {\text{C }}} \right) = 2{\text{ days}} \cr & \left( {{\text{B}} + {\text{C }}} \right) = 2 \times \frac{{10}}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{20}}{3}{\text{ days}} \cr & \frac{1}{2}\left( {{\text{A}} + {\text{B}} + {\text{C }}} \right) = 2{\text{ days}} \cr & {\text{A}} + {\text{B}} + {\text{C}} = {\text{4 days}} \cr} $$
L.C.M of total work = 20
One day work of A + B + C = $$\frac{{20}}{4}$$ = 5 unit/day
One day work of B + C = $$\frac{{20}}{{\frac{{20}}{3}}}$$ = 3 unit/day
A = 5 - 3 = 2
A alone will complete the work
$$\eqalign{ & = \frac{{20}}{2}{\text{days}} \cr & = {\text{10 days}} \cr} $$
46. Ayesha can complete a piece of work in 16 days. Amita can complete the same piece of work in 8 days. If both of them work together in how many days can they complete the same piece of work ?
a) $${\text{4}}\frac{2}{5}{\text{ days}}$$
b) $${\text{5}}\frac{1}{3}{\text{ days}}$$
c) $${\text{6 days}}$$
d) $${\text{12 days}}$$
Discussion
Explanation: Ayesha's 1 day's work $$ = \frac{1}{{16}}$$
Amita's 1 day's work $$ = \frac{1}{{8}}$$
(Ayesha + Amitha)'s 1 day's work
$$\eqalign{ & = {\frac{1}{{16}} + \frac{1}{8}} \cr & = \frac{3}{{16}} \cr} $$
Both together can complete the work in
$$\eqalign{ & = \frac{{16}}{3} \cr & = 5\frac{1}{3}{\text{ days}} \cr} $$
47. A can complete a certain work in 4 minutes, B in 5 minutes, C in 6 minutes, D in 10 minutes and E in 12 minutes. The average number of units of work completed by them per minute will be =
a) 0.16
b) 0.40
c) 0.80
d) None of above
Discussion
Explanation:
$$\eqalign{ & {\text{Required average,}} \cr & = \frac{{ {\frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{{10}} + \frac{1}{{12}}} }}{5} \cr & = {\frac{{48}}{{60}} \times \frac{1}{5}} \cr & = \frac{4}{{25}} \cr & = 0.16 \cr} $$
48. A daily-wages labourer was engaged for a certain number of days for Rs. 5750, but being absent on some of those days he paid only Rs. 5000. What were his maximum possible daily wages ?
a) Rs. 125
b) Rs. 250
c) Rs. 375
d) Rs. 500
Discussion
Explanation: Maximum possible daily wage
= HCF of Rs. 5750 and Rs. 5000
= Rs. 250
49. A and B together can do a piece of work in 8 days, B and C together in 10 days, while C and A together in 6 days, if they all work together the work will be completed in ?
a) $${\text{3}}\frac{3}{4}\,{\text{days}}$$
b) $${\text{3}}\frac{3}{7}\,{\text{days}}$$
c) $${\text{5}}\frac{5}{{47}}\,{\text{days}}$$
d) $${\text{4}}\frac{4}{9}\,{\text{days}}$$
Discussion
Explanation: In these type of questions, always take total work as L.C.M. of number of days
L.C.M. of Total Work = 120
One day work of A + B = $$\frac{{120}}{8}$$ = 15 unit/day
One day work of B + C = $$\frac{{120}}{10}$$ = 12 unit/day
One day work of C + A = $$\frac{{120}}{6}$$ = 20 unit/day
Total units per day = 15 + 12 + 20 = 47
Efficiency of :
$$\eqalign{ & 2\left( {{\text{A}} + {\text{B}} + {\text{C}}} \right) = 47 \cr & {\text{A}} + {\text{B}} + {\text{C}} = \frac{{47}}{2} \cr} $$
(A + B + C) will complete the whole work in
$$\eqalign{ & = \frac{{120}}{{\frac{{47}}{2}}} \cr & = \frac{{240}}{{47}} \cr & = 5\frac{5}{{47}}{\text{days}} \cr} $$
50. A and B together can complete a piece of work in 8 days, B alone can complete that work in 12 days. B alone worked for four days. After that how long will A alone takes to complete the work ?
a) 15 days
b) 18 days
c) 16 days
d) 20 days
Discussion
Explanation: L.C.M. of total work = 24
One day work of A + B = $$\frac{{24}}{8}$$ = 3 unit/day
B's 1 day work = $$\frac{{24}}{12}$$ = 2 units/days
A's 1 day work = 3 - 2 = 1 units/days
4 days work of B = 4 × 2 = 8 units/days
Work left = 24 - 8 = 16 units
A will complete the remaining work in
$$\eqalign{ & = \frac{{{\text{16 units}}}}{{{\text{1 unit/day}}}} \cr & = {\text{16 days}} \cr} $$
51. A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?
a) 40
b) 50
c) 54
d) 60
Discussion
Explanation:
$$\eqalign{ & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{20}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{30}} \times 20} = \frac{2}{3} \cr & {\text{Remaining}}\,{\text{work}} \cr & = {1 - \frac{2}{3}} = \frac{1}{3} \cr & {\text{Now}},\frac{1}{3}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}}\,{\text{20}}\,{\text{days}} \cr & {\text{The}}\,{\text{whole}}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}} \cr & {20 \times 3} = 60\,days \cr} $$
52. P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?
a) $$5\frac{5}{{11}}$$
b) $$5\frac{6}{{11}}$$
c) $$6\frac{5}{{11}}$$
d) $$6\frac{6}{{11}}$$
Discussion
Explanation:
$$\eqalign{ & {\text{P}}\,{\text{can}}\,{\text{complete}}\,{\text{the}}\,{\text{work}} \cr & = \,\left( {12 \times 8} \right){\text{hrs}}{\text{.}} = 96\,{\text{hrs}}{\text{.}} \cr & {\text{Q}}\,{\text{can}}\,{\text{complete}}\,{\text{the}}\,{\text{work}} \cr & = \left( {8 \times 10} \right){\text{hrs}}{\text{.}} = 80\,{\text{hrs}}{\text{.}} \cr & {\text{P's}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} = \frac{1}{{96}}\,{\text{and}} \cr & {\text{Q's}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} = \frac{1}{{80}} \cr & \left( {{\text{P + Q}}} \right){\text{'s}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} \cr & = {\frac{1}{{96}} + \frac{1}{{80}}} = \frac{{11}}{{480}} \cr & {\text{So,}}\,{\text{both}}\,{\text{P}}\,{\text{and}}\,{\text{Q}}\,{\text{will}}\,{\text{finish}}\,{\text{the}}\,{\text{work}} \cr & = {\frac{{480}}{{11}}} {\text{ hrs}}{\text{.}} \cr & {\text{Number}}\,{\text{of}}\,{\text{days}}\,{\text{of}}\,{\text{8}}\,{\text{hours}}\,{\text{each}} \cr & {\frac{{480}}{{11}} \times \frac{1}{8}} = \frac{{60}}{{11}}{\text{days}} = 5\frac{5}{{11}}{\text{days}} \cr} $$
53. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
a) 3
b) 5
c) 7
d) Cannot be determined
Discussion
Explanation:
$$\eqalign{ & 1\,woman's\,1\,day's\,work = \frac{1}{{70}} \cr & {\text{1}}\,{\text{child's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{140}} \cr & \left( {{\text{5}}\,{\text{women + 10}}\,{\text{children}}} \right){\text{'s}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{5}{{70}} + \frac{{10}}{{140}}} = {\frac{1}{{14}} + \frac{1}{{14}}} = \frac{1}{7} \cr & {\text{5}}\,{\text{women}}\,{\text{and}}\,{\text{10}}\,{\text{chidren}}\,{\text{will}}\,{\text{complete}}\,{\text{the}}\,{\text{work}}\,{\text{in}}\,{\text{7}}\,{\text{days}} \cr} $$
54. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
a) 6 Days
b) 10 Days
c) 15 Days
d) 20 Days
Discussion
Explanation:
$$\eqalign{ & {\text{work}}\,{\text{done}}\,{\text{by}}\,{\text{X}}\,{\text{in}}\,{\text{4}}\,{\text{days}} \cr & = {\frac{1}{{20}} \times 4} = \frac{1}{5} \cr & {\text{Remaining}}\,{\text{work}} \cr & = {1 - \frac{1}{5}} = \frac{4}{5} \cr & \left( {{\text{X + Y}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{20}} + \frac{1}{{12}}} = \frac{8}{{60}} = \frac{2}{{15}} \cr & \frac{2}{{15}}{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{X}}\,{\text{and}}\,{\text{Y}}\,{\text{in}}\,{\text{1}}\,{\text{day}}. \cr & \,\frac{4}{5}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{X}}\,{\text{and}}\,{\text{Y}}\,{\text{in}} \cr & {\frac{{15}}{2} \times \frac{4}{5}} = 6\,{\text{days}} \cr & {\text{Hence,}}\,{\text{total}}\,{\text{time}}\,{\text{taken}} \cr & = \left( {6 + 4} \right)\,{\text{days}} \cr & = 10\,{\text{days}} \cr} $$
55. A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
a) 11 days
b) 13 days
c) $$20\frac{3}{{17}}$$ days
d) None of these
Discussion
Explanation:
$$\eqalign{ & {\text{Ratio}}\,{\text{of}}\,{\text{times}}\,{\text{taken}}\,{\text{by}}\,{\text{A}}\,{\text{and}}\,{\text{B}} \cr & = 100:130 = 10:13 \cr & {\text{Suppose}}\,{\text{B}}\,{\text{takes}}\,x\,{\text{days}}\,{\text{to}}\,{\text{do}}\,{\text{the}}\,{\text{work}} \cr & {\text{Then}},10:13::23:x \cr & x = {\frac{{23 \times 13}}{{10}}} \cr & x = \frac{{299}}{{10}} \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{23}} \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{{10}}{{299}} \cr & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{23}} + \frac{{10}}{{299}}} \cr & = \frac{{23}}{{299}} \cr & = \frac{1}{{13}} \cr & A\,{\text{and}}\,{\text{B}}\,{\text{together}}\,{\text{can}}\,{\text{complete}}\,{\text{the}}\,{\text{work}}\,{\text{in}}\,{\text{13}}\,{\text{days}}{\text{.}} \cr} $$
56. Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
a) 7 hours 30 minutes
b) 8 hours
c) 8 hours 15 minutes
d) 8 hours 25 minutes
Discussion
Explanation:
$$\eqalign{ & {\text{Number}}\,{\text{of}}\,{\text{pages}}\,{\text{typed}}\,{\text{by}}\,{\text{Ravi}}\,{\text{in}}\,{\text{1}}\,{\text{hour}} = \cr & \frac{{32}}{6} = \frac{{16}}{3} \cr & {\text{Number}}\,{\text{of}}\,{\text{pages}}\,{\text{typed}}\,{\text{by}}\,{\text{Kumar}}\,{\text{in}}\,{\text{1}}\,{\text{hour}} = \cr & \frac{{40}}{5} = 8 \cr & {\text{Number}}\,{\text{of}}\,{\text{pages}}\,{\text{typed}}\,{\text{by}}\,{\text{both}}\,{\text{in}}\,{\text{1}}\,{\text{hour}} = \cr & {\frac{{16}}{3} + 8} = \frac{{40}}{3} \cr & {\text{Time}}\,{\text{taken}}\,{\text{by}}\,{\text{both}}\,{\text{to}}\,{\text{type}}\,{\text{110}}\,{\text{pages}} \cr & = {110 \times \frac{3}{{40}}} {\text{hours}} \cr & = 8\frac{1}{4}\,{\text{hours}}\,{\text{or}}\,{\text{8}}\,{\text{hours}}\,{\text{15}}\,{\text{minutes}} \cr} $$
57. A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:
a) $$\frac{1}{{24}}$$ day
b) $$\frac{7}{{24}}$$ day
c) $$3\frac{3}{7}$$ days
d) 4 days
Discussion
Explanation:
$$\eqalign{ & (A + B + C)'s\,1\,{\text{day's work}} \cr & = {\frac{1}{{24}} + \frac{1}{6} + \frac{1}{{12}}} = \frac{7}{{24}} \cr} $$
So, all the three together will complete the job in
$$ {\frac{{24}}{7}} {\text{ days}} = 3\frac{3}{7}{\text{ days}}$$
58. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:
a) 15
b) 16
c) 18
d) 25
Discussion
Explanation: Ratio of times taken by Sakshi and Tanya
= 125 : 100
= 5 : 4
Suppose Tanya takes x days to do the work
5 : 4 :: 20 : x
$$x = {\frac{{4 \times 20}}{5}} $$
x = 16 days
Tanya takes 16 days to complete the work
59. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:
a) 4 Days
b) 6 Days
c) 8 Days
d) 12 Days
Discussion
Explanation:
$$\eqalign{ & {\text{Suppose}}\,{\text{A,}}\,{\text{B}}\,{\text{and}}\,{\text{C}}\,{\text{take}} \cr & x,\,\frac{x}{2},\,\frac{x}{3}\,{\text{days}}\,{\text{respectively}}\,{\text{to}}\,{\text{finish}}\,{\text{the}}\,{\text{work}} \cr & {\text{Then}},\, {\frac{1}{x} + \frac{2}{x} + \frac{3}{x}} = \frac{1}{2} \cr & \frac{6}{x} = \frac{1}{2} \cr & x = 12 \cr & {\text{So,}}\,{\text{B}}\,{\text{takes}}\, {\frac{{12}}{2}} \cr & = 6\,{\text{days}}\,{\text{to}}\,{\text{finish}}\,{\text{the}}\,{\text{work}} \cr} $$
60. A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :
a) 8 days
b) 10 days
c) 12 days
d) 15 days
Discussion
Explanation:
$$\eqalign{ & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{15}} + \frac{1}{{10}}} = \frac{1}{6} \cr & {\text{Work}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{and}}\,{\text{B}}\,{\text{in}}\,{\text{2}}\,{\text{days}} \cr & = {\frac{1}{6} \times 2} = \frac{1}{3} \cr & {\text{Remaining}}\,{\text{work}} \cr & = {1 - \frac{1}{3}} = \frac{2}{3} \cr & \frac{1}{{15}}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}}\,{\text{1}}\,{\text{day}} \cr & \frac{2}{3}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{a}}\,{\text{in}} \cr & {15 \times \frac{2}{3}} = 10\,{\text{days}} \cr & {\text{Hence,}}\,{\text{the}}\,{\text{total}}\,{\text{time}}\,{\text{taken}} \cr & = {10 + 2} = 12\,{\text{days}} \cr} $$
61. A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:
a) 15 Days
b) 20 Days
c) 25 Days
d) 30 Days
Discussion
Explanation:
$$\eqalign{ & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{10}} \cr & {\text{C's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{50}} \cr & \left( {{\text{A + B + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{10}} + \frac{1}{{50}}} = \frac{6}{{50}} = \frac{3}{{25}}........\left( {\text{i}} \right) \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \left( {{\text{B + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}}\,........\left( {{\text{ii}}} \right) \cr & {\text{From}}\,\left( {\text{i}} \right)\,{\text{and}}\,\left( {{\text{ii}}} \right){\text{,we}}\,{\text{get}}:2 \times \left( {{\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}}} \right) \cr & = \frac{3}{{25}} \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{3}{{50}} \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}}\left( {\frac{1}{{10}} - \frac{3}{{50}}} \right) \cr & = \frac{2}{{50}} = \frac{1}{{25}} \cr & {\text{B}}\,\,{\text{alone}}\,{\text{could}}\,{\text{do}}\,{\text{the}}\,{\text{work}}\,{\text{in}}\,{\text{25}}\,{\text{days}} \cr} $$
62. A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
a) 23 days
b) 37 days
c) $$37\frac{1}{2}$$ days
d) 40 days
Discussion
Explanation:
$$\eqalign{ & {\text{Whole}}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}} \cr & = {20 \times \frac{5}{4}} = 25\,{\text{days}} \cr & {\text{Now}},\,\left( {1 - \frac{4}{5}} \right) \cr & \frac{1}{5}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{and}}\,{\text{B}}\,{\text{in}}\,{\text{3}}\,{\text{days}} \cr & {\text{Whole}}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{and}}\,{\text{B}}\,{\text{in}} \cr & = \left( {3 \times 5} \right) = 15\,{\text{days}} \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{25}}, \cr & \left( {{\text{A + B}}} \right)\,{\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{15}} \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{15}} - \frac{1}{{25}}} = \frac{4}{{150}} = \frac{2}{{75}} \cr & {\text{B}}\,\,{\text{alone}}\,{\text{would}}\,{\text{do}}\,{\text{the}}\,{\text{work}}\,{\text{in}} \cr & \frac{{75}}{2} = 37\frac{1}{2}\,{\text{days}} \cr} $$
63. A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?
a) 11:30 A.M.
b) 12 Noon
c) 12:30 P.M.
d) 1:00 P.M.
Discussion
Explanation:
$$\eqalign{ & \left( {{\text{P + Q + R}}} \right){\text{'s}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} \cr & = {\frac{1}{8} + \frac{1}{{10}} + \frac{1}{{12}}} = \frac{{37}}{{120}} \cr & {\text{Work}}\,{\text{done}}\,{\text{by}}\,{\text{P,}}\,{\text{Q}}\,{\text{and}}\,{\text{R}}\,{\text{in}}\,{\text{2}}\,{\text{hours}} \cr & = {\frac{{37}}{{120}} \times 2} = \frac{{37}}{{60}} \cr & {\text{Remaining}}\,{\text{work}} = {1 - \frac{{37}}{{60}}} = \frac{{23}}{{60}} \cr & \left( {{\text{Q + R}}} \right){\text{'s}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} \cr & = {\frac{1}{{10}} + \frac{1}{{12}}} = \frac{{11}}{{60}} \cr & \frac{{11}}{{60}}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{Q}}\,\,{\text{and}}\,{\text{R}}\,{\text{in}}\,{\text{1}}\,{\text{hour}} \cr & \frac{{23}}{{60}}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{Q}}\,{\text{and}}\,{\text{R}}\,{\text{in}} \cr & = {\frac{{60}}{{11}} \times \frac{{23}}{{60}}} = \frac{{23}}{{11}}\,{\text{hours}} \approx 2\,{\text{hours}} \cr & {\text{The}}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{finished}}\,{\text{approximately}} \cr & {\text{2}}\,{\text{hours}}\,{\text{after}}\,{\text{11}}\,{\text{A}}{\text{.M}}{\text{.,}}\,{\text{i}}{\text{.e}}{\text{.,}}\,{\text{around}}\,{\text{1}}\,{\text{P}}{\text{.M}}{\text{.}} \cr} $$
64. A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
a) 5
b) $$5\frac{1}{2}$$
c) 6
d) 8
Discussion
Explanation:
$$\eqalign{ & {\text{B's}}\,{\text{10}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{15}} \times 10} = \frac{2}{3} \cr & {\text{Remaining}}\,{\text{work}} \cr & = {1 - \frac{2}{3}} = \frac{1}{3} \cr & \frac{1}{{18}}{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}}\,{\text{1}}\,{\text{day}} \cr & \frac{1}{3}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}} \cr & {18 \times \frac{1}{3}} = 6\,{\text{days}} \cr} $$
65. 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
a) 35
b) 40
c) 45
d) 50
Discussion
Explanation Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y
Then, 4x + 6y = $$\frac{1}{8}$$ and 3x + 7y = $$\frac{1}{{10}}$$
On solving the two equations,
$$x = \frac{{11}}{{400}},\,\,\,y = \frac{1}{{400}}$$
1 woman's 1 day's work = $$\frac{1}{{400}}$$
10 women's 1 day's work = $$ {\frac{1}{{400}} \times 10} $$ = $$\frac{1}{{40}}$$
10 women will complete the work in 40 days
66. A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
a) 18 days
b) 24 days
c) 30 days
d) 36 days
Discussion
Explanation:
$$\eqalign{ & {\text{2(A + B + C)'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{30}} + \frac{1}{{24}} + \frac{1}{{20}}} \cr & = \frac{{15}}{{120}} = \frac{1}{8} \cr & \left( {{\text{A + B + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \frac{1}{{2 \times 8}} = \frac{1}{{16}} \cr & {\text{Work}}\,{\text{done}}\,{\text{by}}\,{\text{A,}}\,{\text{B,}}\,{\text{C}}\,{\text{in}}\,{\text{10}}\,{\text{days}} \cr & = \frac{{10}}{{16}} = \frac{5}{8} \cr & {\text{Remaining}}\,{\text{work}} \cr & = {1 - \frac{5}{8}} = \frac{3}{8} \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{16}} - \frac{1}{{24}}} = \frac{1}{{48}} \cr & \frac{1}{{48}}\,{\text{work}}\,{\text{isdone}}\,{\text{by}}\,{\text{A}}\,{\text{in}}\,{\text{1}}\,{\text{day}} \cr & \frac{3}{8}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}} \cr & {48 \times \frac{3}{8}} = 18\,{\text{days}} \cr} $$
67. A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :
a) 4 days
b) 6 days
c) 8 days
d) 18 days
Discussion
Explanation:
$$\eqalign{ & {\text{Ration}}\,{\text{of}}\,{\text{rates}}\,{\text{of}}\,{\text{working}}\,{\text{of}}\,{\text{A}}\,{\text{and}}\,{\text{B}} \cr & = 2:1 \cr & {\text{So,}}\,{\text{ratio}}\,{\text{of}}\,{\text{times}}\,{\text{taken}} = 1:2 \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{12}} \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \frac{1}{3};\,({\text{2 times}}\,{\text{of}}\,{\text{B's}}\,{\text{work}}) \cr & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{6} + \frac{1}{{12}}} = \frac{3}{{12}} = \frac{1}{4} \cr & {\text{A}}\,{\text{and}}\,{\text{B}}\,{\text{together}}\,{\text{can}}\,{\text{finish}}\,{\text{the}},{\text{work}}\,{\text{in}}\,{\text{4}}\,{\text{days}}{\text{.}}\, \cr} $$
68. Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
a) 3 : 4
b) 4 : 3
c) 5 : 3
d) Data inadequate
Discussion
Explanation:
$$\eqalign{ & \left( {20 \times 16} \right){\text{women}}\,{\text{can}}\,{\text{complete}}\,{\text{the}}\,{\text{work}}\,{\text{in}}\,{\text{1}}\,{\text{day}} \cr & {\text{1}}\,{\text{woman's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{320}} \cr & \left( {16 \times 15} \right)\,{\text{men}}\,{\text{can}}\,{\text{complete}}\,{\text{the}}\,{\text{work}}\,{\text{in}}\,{\text{1}}\,{\text{day}} \cr & {\text{1}}\,{\text{man's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{240}} \cr & {\text{So,}}\,{\text{required}}\,{\text{ratio}} \cr & = \frac{1}{{240}}:\frac{1}{{320}} \cr & = \frac{1}{3}:\frac{1}{4} \cr & = 4:3\,\left( {{\text{cross}}\,{\text{multiplied}}} \right) \cr} $$
69. A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :
a) 4 days
b) 6 Days
c) 8 Days
d) 12 Days
Discussion
Explanation:
$$\eqalign{ & \left( {{\text{A + B + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{6} \cr & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{8} \cr & \left( {{\text{B + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{12}} \cr & \left( {{\text{A + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \left( {2 \times \frac{1}{6}} \right) - \left( {\frac{1}{8} + \frac{1}{{12}}} \right) \cr & = {\frac{1}{3} - \frac{5}{{24}}} \cr & = \frac{3}{{24}} \cr & = \frac{1}{8} \cr }$$
A and C together will do the work in 8 days
70. A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:
a) 5 days
b) 6 days
c) 10 days
d) $$10\frac{1}{2}$$ days
Discussion
Explanation:
$$\eqalign{ & \left( {{\text{B + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{9} + \frac{1}{{12}}} = \frac{7}{{36}} \cr & {\text{Work}}\,{\text{done}}\,{\text{by}}\,{\text{B}}\,{\text{and}}\,{\text{C}}\,{\text{in}}\,{\text{3}}\,{\text{days}} \cr & = {\frac{7}{{36}} \times 3} = \frac{7}{{12}} \cr & {\text{Remaining}}\,{\text{work}} \cr & = {1 - \frac{7}{{12}}} = \frac{5}{{12}} \cr & \frac{1}{{24}}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}}\,{\text{1}}\,{\text{day}} \cr & \frac{5}{{12}}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}} \cr & {24 \times \frac{5}{{12}}} = 10\,{\text{days}} \cr} $$
71. Computer A takes 3 minutes to process an input while computer B takes 5 minutes. If computers A, B and C can process an average of 14 inputs in one hour, how many minutes does computer C alone take to process one input ?
a) 4 minutes
b) 6 minutes
c) 10 minitus
d) None of above
Discussion
Explanation: Number of units processed by computer A in 1 minute
$$ = \frac{1}{3}$$
Number of units processed by computer B in 1 minute
$$ = \frac{1}{5}{\text{ }}$$
Number of units processed by computer A, B and C in 1 minute
$$\eqalign{ & = \frac{{14 \times 3}}{{60}} \cr & {\text{ = }}\frac{7}{{10}} \cr} $$
Number of units processed by computer C in 1 minute
$$\eqalign{ & = \frac{7}{{10}} - \left( {\frac{1}{3} + \frac{1}{5}} \right) \cr & = \frac{7}{{10}} - \frac{8}{{15}} \cr & = \frac{5}{{30}} \cr & = \frac{1}{6} \cr} $$
Computer C takes 6 minutes to process one input alone.
72. 5 men and 2 women working together can do four times as much work per hour as a men and a women together. The work done by a men and a women should be in the ratio ?
a) 1 : 2
b) 2 : 1
c) 4 : 1
d) 1 : 3
Discussion
Explanation:
$$\frac{{{\text{5 men}} + {\text{2 women}}}}{{4{\text{work}}}}$$ = $$\left( {1{\text{ men}} + {\text{1 women}}} \right)$$
$$5{\text{ men}} + {\text{2 women}}$$ = $${\text{4 men}} + {\text{4 women}}$$
$$\eqalign{ & {\text{1 men}} = {\text{2 women}} \cr & \frac{{{\text{Men}}}}{{{\text{Women}}}} = \frac{2}{1} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{M}}:{\text{W}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2:1 \cr} $$
73. If 40 men or 60 women or 80 children can do a piece of work in 6 months, then 10 men, 10 women and 10 children together do the work in ?
a) $${\text{5}}\frac{6}{{13}}{\text{ months}}$$
b) $${\text{6 months}}$$
c) $${\text{5}}\frac{7}{{13}}{\text{ months}}$$
d) $${\text{11}}\frac{1}{{13}}{\text{ months}}$$
Discussion
Explanation: 40 men = 60 women = 80 children
2 men = 3 women = 4 children
2 men = 3 women
1 women = $$\frac{2}{3}$$ men → 10 women
$$ \to \frac{2}{3} \times 10 = \frac{{20}}{3}{\text{ men}}$$
Similarly,
2 men = 4 children
1 children = $$\frac{1}{2}$$ men → 10 children
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{10}}{2} = {\text{5 men}}$$
10 men = 10 women = 10 children
$$\eqalign{ & {\text{10 men}} + \frac{{20}}{3} + 5 \cr & \Rightarrow \frac{{30 + 20 + 15}}{3} \cr} $$
10 men + 10 women + 10 children = $$\frac{{65}}{3}$$ men
40 men can do a piece of work in 6 months
1 men can do a piece of work in 6 × 40
$$\frac{{65}}{3}$$ men can do a piece of work in
$$\eqalign{ & = \frac{{6 \times 40}}{{\frac{{65}}{3}}} \cr & = 11\frac{1}{{13}}{\text{ months}} \cr} $$
74. Two workers A and B working together completed a job in 5 days. If A had worked twice as efficiently as he actually did, the work would have been completed in 3 days. To complete the job alone, A would require?
a) $${\text{5}}\frac{1}{5}{\text{ days}}$$
b) $${\text{6}}\frac{1}{4}{\text{ days}}$$
c) $${\text{7}}\frac{1}{2}{\text{ days}}$$
d) $${\text{8}}\frac{3}{4}{\text{ days}}$$
Discussion
Explanation: L.C.M. of Total Work = 15
One day work of A + B = $$\frac{{15}}{5}$$ = 3 unit/day
One day work of (2A + B) = $$\frac{{15}}{3}$$ = 5 unit/day
Assume A's efficiency is 2 units, B's is 1 unit.
It satisfies the equation of both cases
Actual efficiency of A is 2 units/day
A alone can complete the work in
$$\eqalign{ & = \frac{{{\text{Total work}}}}{{{\text{Efficiency}}}} \cr & = \frac{{15}}{2} \cr & = 7\frac{1}{2}{\text{days}} \cr} $$
75. 3 men and 7 women can do a job in 5 days, while 4 men and 6 women can do it in 4 days. The number of days required for a group of 10 women working together, at the same rate as before, to finish the same job in ?
a) 30 days
b) 36 days
c) 20 days
d) 40 days
Discussion
Explanation (3 men + 7 women) × 5 days = (4 men + 6 women) × 4 days
1 men = 11 women
∴ 3 men + 7 women
(3 × 11) women + 7 women
= 40 women
40 women can do a work in 5 days
1 women can do a work in (5 × 40) days
10 women can do a work in = $$\frac{{5 \times 40}}{{10}}$$ = 20 days
76. Tapas works twice as fast as Mihir. If both of them together complete a work in 12 days, Tapas alone can complete it in ?
a) 15 days
b) 18 days
c) 20 days
d) 24 days
Discussion
Explanation:
| Tapas | : | Mihir | |
| Efficiency units/day |
2 | : | 1 |
Tapas alone complete the whole work in
$$\eqalign{ & = \frac{{36}}{2} \cr & = 18{\text{ days}} \cr} $$
77. 2 men and 3 women together or 4 men can complete a piece of work in 20 days. 3 men and 3 women will complete the same work in =
a) 12 day
b) 16 day
c) 18 days
d) 19 days
Discussion
Explanation: According to the question,
$$\eqalign{ & {\text{2m}} + {\text{3w}} = {\text{4m}} \cr & {\text{3w}} = {\text{4m}} - {\text{2m }} \cr & {\text{3w}} = {\text{2m}} \cr & {\text{3m}} + {\text{3w}} = {\text{3m}} + {\text{2m}} \cr & {\text{3m}} + {\text{3w}} = {\text{5m}} \cr} $$
4 men can do work in 20 days
1 men can do work in 20 × 4 days
5 men can do work in $$\frac{{{\text{20}} \times {\text{4}}}}{5}$$ = 16 days
78. Twenty women together can complete a piece of work in 16 days, 16 men together can complete the same work in 15 days. The ratio of the working capacity of a man to that of a women is =
a) 3 : 4
b) 4 : 3
c) 5 : 3
d) 4 : 5
Discussion
Explanation:
$$\eqalign{ & {\text{20 w}} \times {\text{16}} = {\text{16 m}} \times {\text{15}} \cr & {\text{20 w}} = {\text{15 m}} \cr & {\text{4 w}} = {\text{3 m}} \cr & \frac{{\text{m}}}{{\text{w}}} = \frac{4}{3} \cr & {\text{Man}}:{\text{Women}} \cr & \,\,\,\,\,\,4:3 \cr} $$
79. A conveyor belt delivers baggage at the rate of 3 tons in 5 minutes and second conveyor belt delivers baggage at the rate of 1 ton in 2 minutes. How much time will it take to get
33 tons of baggage delivered using both the conveyor belts together ?
a) 25 minutes 30 seconds
b) 30 minutes
c) 35 minutes
d) 45 minutes
Discussion
Explanation: Baggage delivered by first belt in 1 minute
$$ = \left( {\frac{3}{5}} \right){\text{tons}}$$
Baggage delivered by second belt in 1 minute
$$ = \left( {\frac{1}{2}} \right){\text{tons}}$$
Baggage delivered by both belt in 1 minute
$$\eqalign{ & = \left( {\frac{3}{5} + \frac{1}{2}} \right){\text{tons}} \cr & = \frac{{11}}{{10}}{\text{ tons}} \cr & {\text{Required time}} \cr & = \left( {33 \div \frac{{11}}{{10}}} \right){\text{ minutes}} \cr & = \left( {33 \times \frac{{10}}{{11}}} \right){\text{minutes}} \cr & = {\text{30 minutes}} \cr} $$
80. A manufacturer builds a machine which will address 500 envelopes in 8 minutes. He wishes to build another machine so that when both are operating together they will address 500 envelopes in 2 minutes. The equation used to find how many minutes x it would require the second machine to address 500 envelopes alone, is =
a) $$8 - x = 2$$
b) $$\frac{1}{8} + \frac{1}{x} = \frac{1}{2}$$
c) $$\frac{{500}}{8} + \frac{{500}}{x} = 500$$
d) $$\frac{x}{2} + \frac{x}{8} = 1$$
Discussion
Explanation: Number of envelopes addressed by first machine in 1 minute
$$ = \frac{{500}}{8}$$
Number of envelopes addressed by second machine in 1 minute
$$ = \frac{{500}}{x}$$
Number of envelopes addressed by both machine in 1 minute
$$\eqalign{ & {\text{ = }}\frac{{500}}{2} \cr & \frac{{500}}{8} + \frac{{500}}{x} = \frac{{500}}{2} \cr & \frac{1}{8} + \frac{1}{x} = \frac{1}{2} \cr} $$
81. P, Q and R are three typists who working simultaneously can type 216 pages in 4 hours. In one hour, R can type as many pages more than Q as Q can type more than P. During a period of five hours, R can type as many pages as P can during seven hours. How many pages does each of them type per hour ?
a) 14, 17, 20
b) 15, 17, 22
c) 15, 18, 21
d) 16, 18, 22
Discussion
Explanation: Let the number of pages typed in one hour by P, Q and R be x, y and z respectively
$$\eqalign{ & \Rightarrow x + y + z = \frac{{216}}{4} \cr & \Rightarrow x + y + z = 54z.....{\text{(i)}} \cr & {\text{ }}z - y = y - x \cr & \Rightarrow 2y = x + z.....{\text{(ii)}} \cr & {\text{ }}5z = 7x \cr & \Rightarrow x = \frac{5}{7}z......{\text{(iii)}} \cr} $$
On Solving (i), (ii) and (iii)
$$\eqalign{ & x = 15, \cr & y = 18,{\text{ }} \cr & z = 21 \cr} $$
82. Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages ?
a) 7 hours 30 minutes
b) 8 hours
c) 8 hours 15 minutes
d) 8 hours 25 minutes
Discussion
Explanation: Number of pages typed by Ronald in 1 hour
$$\eqalign{ & = \frac{{32}}{6} \cr & = \frac{{16}}{3} \cr} $$
Number of pages typed by Elan in 1 hour
$$\eqalign{ & = \frac{{40}}{5} \cr & = 8 \cr} $$
Number of pages typed by both in 1 hour
$$\eqalign{ & = \left( {\frac{{16}}{3} + 8} \right) \cr & = \frac{{40}}{3} \cr} $$
Time taken by both to type 110 pages
$$\eqalign{ & {\text{ = }}\left( {100 \times \frac{3}{{40}}} \right){\text{hours}} \cr & = 8\frac{1}{4}{\text{hours}} \cr & = {\text{8 hours 15 minutes}} \cr} $$
83. Cloth Makers Inc. has p spindles, each of which can produce q metres of cloth on an average in r minutes. If the spindles are made to run with no interruption, then how many hours will it take for 20000 metres of cloth to be produced ?
a) $$\frac{{20000{\text{pq}}}}{{\text{r}}}$$
b) $$\frac{{20000{\text{rq}}}}{{\text{p}}}$$
c) $$\frac{{20000{\text{r}}}}{{{\text{pq}}}}$$
d) $$\frac{{20000{\text{r}}}}{{60{\text{pq}}}}$$
Discussion
Explanation: Length of the cloth produced in 1 hour
$$\eqalign{ & {\text{ = }}\left( {\frac{{{\text{pq}}}}{{\text{r}}} \times 60} \right){\text{ m }} \cr & = \left( {\frac{{60{\text{pq}}}}{{\text{r}}}} \right){\text{ m}} \cr & {\text{Required time}} \cr & = \left( {20000 \div \frac{{60{\text{pq}}}}{{\text{r}}}} \right){\text{ hours }} \cr & {\text{ = }}\left( {\frac{{20000{\text{r}}}}{{60{\text{pq}}}}} \right){\text{ hours}} \cr} $$
84. One man or two women or three boys can do a piece of work in 88 days. One man, one woman and one boy will do it in ?
a) 44 days
b) 24 days
c) 48 days
d) 20 days
Discussion
Explanation:
$$\eqalign{ & {\text{1 man}} = {\text{2 women}} = {\text{3 boys}} \cr & {\text{1 man}} = {\text{2 women}} \cr & {\text{1 man}} = {\text{3 boys}} \cr & \frac{1}{2}{\text{ man}} = 1{\text{ women}} \cr & \frac{1}{3}{\text{ man}} = {\text{1 boys}} \cr & = {\text{1 man}} = 1{\text{ woman}} = 1{\text{ boys}} \cr & = {\text{1 man}} = \frac{1}{2}{\text{man}} = \frac{1}{3}{\text{ man}} \cr & = \frac{{11}}{6}{\text{ man}} \cr} $$
1 man can complete a work in 88 days
$$\eqalign{ & \frac{{11}}{6}{\text{man can complete a work in}} \cr & = \frac{{88}}{{\frac{{11}}{6}}}\, = 48{\text{ days }} \cr} $$
85. 15 men can finish a piece of work in 20 days, however it takes 24 women to finish it in 20 days. If 10 men and 8 women undertake to complete the work, then they will take ?
a) 20 days
b) 30 days
c) 10 days
d) 15 days
Discussion
Explanation
$$\eqalign{ & {\text{15 men}} = {\text{20 days}} \cr & {\text{300 men}} = 1{\text{ days}}.....{\text{(i)}} \cr & {\text{24 women}} = {\text{20 days}} \cr & {\text{480 men}} = 1{\text{ days}}......{\text{(ii)}} \cr & {\text{Compare equation (i) and (ii)}} \cr & {\text{300 men}} = 480{\text{ women}} \cr & {\text{5 men}} = 8{\text{ women}}.....{\text{(iii)}} \cr & {\text{10 men}} + 8{\text{ women}} = ? \cr & {\text{10 men}} + {\text{5 men}} = ? \cr & 15\,{\text{men}} = ? \cr} $$
$${\text{15 men}} \times {\text{20 days}}$$ = $${\text{15 men}}$$ $$ \times $$ $$x{\text{ days}}$$
$$x$$ = 20 days
86. A is thrice good a workman as B and therefore is able to finish a job in 40 days less than B. Working together they can do it in:
a) 15 days
b) 16 days
c) 18 days
d) 20 days
Discussion
Explanation: A is thrice good workman as B.
A = 3B
Let B can finish work in X days, then A will finish same work in (X - 40) days alone
BX = 3B × (X - 40)
X = 60 days
B can finish work in 60 days, then A can finish the work in 20 days.
One day work of B = $$\frac{1}{{60}}$$
One day work of A = $$\frac{1}{{20}}$$
One day work of (A+B) =
$$\frac{1}{{60}} + \frac{1}{{20}} \Rightarrow \frac{{1 + 3}}{{60}} \Rightarrow \frac{1}{{15}}$$
They can finish work together in 15 days
87. A and B can compete a piece of work in 18 days. They worked together for 12 days and then A left. B alone finished the work in 15 days. If Rs. 1500 be paid for the work then A's share is:
a) Rs. 750
b) Rs. 800
c) Rs. 600
d) Rs. 900
Discussion
Explanation: A and B can complete the work in 18 days, work rate = $$\frac{{100}}{{18}}$$ = 5.55% per day
They together can complete the work in 12 days = 5.55 × 12 = 66.60%
Now, A leaves and B takes another 15 days to complete the whole work, Work rate of B = $$\frac{{33.30}}{{15}}$$ = 2.22% per day
B work for (12 + 15) = 27 days
Work done by B in 27 days = 2.22 × 27 ≈ 60% And So 40% work is done by A. so there share should be 60% and 40% ratio.
A's share = 40% of 1500 = Rs. 600
88. If 3 men or 4 women can plough a field in 43 days, how long will 7 men and 5 women take to plough it?
a) 10 days
b) 11 days
c) 9 days
d) 12 days
Discussion
Explanation: 3 men or 4 women can plough the field in 43 days
3 men = 4 women
1 man = $$\frac{4}{3}$$ women
7 man = $$\frac{{28}}{3}$$ women
7 men and 5 women = $$5 + \frac{{28}}{3}$$ = $$\frac{{43}}{3}$$ women
4 women can plough field in 43 days
1 women can plough in = 43 × 4 days
$$\frac{{43}}{3}$$ women can plough = $$\frac{{43 \times 4 \times 3}}{{43}}$$ = 12 days
89. To complete a piece of work A and B take 8 days, B and C 12 days. A, B and C take 6 days. A and C will take :
a) 7 Days
b) 7.5 Days
c) 8 Days
d) 8.5 Days
Discussion
Explanation: Given (A+B)'s one day's work = $$\frac{1}{8}$$
(B + C)'s one day's work = $$\frac{1}{{12}}$$
(A + B + C) 's 1 day's work = $$\frac{1}{6}$$
Work done by A, alone= (A + B + C) 's 1 day's work - (B + C)'s one day's work
$$ = \frac{1}{6} - \frac{1}{{12}} = \frac{{2 - 1}}{{12}} = \frac{1}{{12}}$$
Work done by C, alone = (A + B + C) 's 1 day's work - (A + B)'s one day’s work
$$ = \frac{1}{6} - \frac{1}{8} = \frac{{4 - 3}}{{24}} = \frac{1}{{24}}$$
⇒ (A + C)’s one day’s work
$$\eqalign{ & = \frac{1}{{12}} + \frac{1}{{24}} \cr & = \frac{{2 + 1}}{{24}} \cr & = \frac{3}{{24}} = \frac{1}{8} \cr} $$
(A + C) will take 8 days to complete the work together
90. Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 20hr. If all pipes are opened simultaneously, then the cistern will be filled in:
a) 7.5 hr
b) 8 hr
c) 8.5 hr
d) 10 hr
Discussion
Explanation: Work done by all the tanks working together in 1 hour,
$$ \Rightarrow \frac{1}{{10}} + \frac{1}{{12}} - \frac{1}{{20}} = \frac{2}{{15}}$$
Tank will be filled in $$\frac{{15}}{2}$$ = 7.5 hour.
91. Three taps A, B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes. How long will the tap C alone take to fill it?
a) 16 minutes
b) 24 minutes
c) 32 minutes
d) 40 minutes
Discussion
Explanation: A, B and C together can fill 100% empty tank in 10 minutes
Work rate of (A + B + C) = $$\frac{{100}}{{10}}$$ = 10% per minute
A alone can fill the tank in 30 minutes
Work rate of A = $$\frac{{100}}{{30}}$$ = 3.33% per minute
B alone can fill the tank in 40 minutes
Work rate of B = $$\frac{{100}}{{40}}$$ = 2.5%
Work rate of (A + B) = 3.33 + 2.5 = 5.83% per minute
Work rate of C,
= Work rate of (A + B + C) - (A + B)
= 10 - 5.83 = 4.17% per minute
C takes = $$\frac{{100}}{{4.17}}$$ ≈ 24 minutes to fill the tank
92. A and B working separately can do a piece of work in 9 and 15 days respectively. If they work for a day alternately, with A beginning, then the work will be completed in:
a) 9 days
b) 10 days
c) 11 days
d) 12 days
Discussion
Explanation: Work rate of A = $$\frac{{100}}{9}$$ = 11.11% work per day
Work rate of B = $$\frac{{100}}{{15}}$$ = 6.66% work per day
They together can do (A + B) = 11.11 + 6.66 ≈ 18% work per day
They are working in alternate day, so we take 2 days = 1 unit of day
Therefore, in one unit of day they can complete 18% of work
(A + B) can complete 90% of work in 5 units of days. i.e. (5 × 18)
And the rest 10% work will be completed by A in Next day
Total number of day = 5 Unit of days + 1 day of A
= 2 × 5 + 1 = 11 days
93. Two pipes A and B can fill a tank in 36 min. and 45 min. respectively. Another pipe C can empty the tank in 30 min. First A and B are opened. After 7 minutes, C is also opened. The tank filled up in:
a) 39 min.
b) 46 min
c) 40 min.
d) 45 min.
Discussion
Explanation: Pipe A can fill empty tank in 36 min.
Pipe A can fill the tank = $$\frac{{100}}{{36}}$$ = 2.77% per minute
Pipe B can fill empty tank in 45 min.
Pipe B can fill the tank = $$\frac{{100}}{{45}}$$ = 2.22% per min.
A and B can together fill the tank
= (2.77 + 2.22) ≈ 5% per minute
So, A and B can fill the tank in 7 min.
= 7 × 5 = 35% of the tank
Rest tank to be filled = 100 - 35 = 65%
C can empty the full tank in 30 min.
C can empty the tank = $$\frac{{100}}{{30}}$$ = 3.33% per min.
C is doing negative work i.e. emptying the tank
A, B and C can together fill the tank,
= 2.77% + 2.22% - 3.33% = 1.67% tank per minute
A, B and C will take time to fill 65% empty tank,
= $$\frac{{65}}{{1.67}}$$ = 39 min. (Approx)
94. Three men A, B, C working together can do a job in 6 hours less time than A alone, in one hour less time than B alone and in one half the time needed by C when working alone. Then A and B together can do the job in:
a) $$\frac{2}{3}$$ hours
b) $$\frac{3}{4}$$ hours
c) $$\frac{3}{2}$$ hours
d) $$\frac{4}{3}$$ hours
Discussion
Explanation: Time taken by A =x hours.
Therefore taken by A, B and C together = (x - 6)
Time taken by B = (x - 5)
Time taken by C = 2(x - 6)
Now, rate of work of A + Rate of work of B + Rate of work of C = Rate of work of ABC.
$$ \frac{1}{x} + \frac{1}{{x - 5}} + \frac{1}{{2\left( {x - 6} \right)}} = \frac{1}{{x - 6}}$$
On solving above equation, x = 3, $$\frac{{40}}{6}$$
When x = 3, the expression (x - 6) becomes negative, thus it's not possible.
$$ x = \frac{{40}}{6}$$
Time taken by A & B together = $$\frac{1}{{\frac{3}{{20}} + \frac{3}{5}}}$$
= $$\frac{4}{3}$$ hours
95. A does half as much work as B in one -sixth of the time.If together they take 10 days to complete a work, how much time shall B take to do it alone?
a) 13.33 days
b) 20 days
c) 30 days
d) 40 days
Discussion
Explanation: Given,
$${\text{A}} \times \frac{1}{6} = {\text{B}} \times \frac{1}{2}$$
A = 3B
Given they together complete the work in 10 days
So, One Day's work of,
(A + B) = $$\frac{{100}}{{10}}$$ = 10%
(3B + B) = 10%
4B = 10%
one day work of B = $$\frac{{10}}{4}$$ = 2.5%
B can complete 100% work in = $$\frac{100}{2.5}$$ = 40 days
96. An employee pays Rs. 26 for each day a worker and forfeits Rs. 7 for each day he idle. At the end of 56 days, if the worker got Rs. 829, for how many days did the worker remain idle?
a) 21 days
b) 15 days
c) 19 days
d) 13 days
Discussion
Explanation: His Per day pay = Rs. 26
Total pay employee got = Rs. 829
Total pay he gets if he did not remain idle a single day,
= 26 × 56 = Rs. 1456
He Forfeits or fined = 1456 - 829 = Rs. 627
Per day he Forfeits Rs. 7 Means per idle day he loses = 26 + 7 = Rs. 33
Total idle days = $$\frac{{627}}{{33}}$$ = 19 days
97. A is 60% more efficient than B. In how many days will A and B working together complete a piece of work which A alone takes 15 days to finish?
a) $$\frac{{124}}{{13}}$$ days
b) $$\frac{{113}}{{13}}$$ days
c) $$\frac{{108}}{{13}}$$ days
d) $$\frac{{120}}{{13}}$$ days
Discussion
Explanation: Given,
A is 60% more efficient of B Means,
$$\eqalign{ & {\text{A}} = {\text{B}} + 60\% \,{\text{of B}} \cr & {\text{A}} = {\text{B}} + \frac{{60{\text{B}}}}{{100}} \cr & {\text{A}} = \frac{{100{\text{B}} + 60{\text{B}}}}{{100}} \cr & {\text{A}} = \frac{{160{\text{B}}}}{{100}} \cr & {\text{A}} = \frac{{8{\text{B}}}}{5} \cr} $$
A can complete whole work in 15 days. So,
One day work of A = $$\frac{1}{{15}}$$
One day work of A = $$\frac{{8{\text{B}}}}{5}$$ = $$\frac{1}{{15}}$$
One day work of B = $$\frac{5}{{120}}$$ = $$\frac{1}{{24}}$$
One day work, (A + B) = $$ \frac{1}{{15}} + \frac{1}{{24}}$$
One day work, (A + B) = $$\frac{{24 + 15}}{{360}}$$ = $$\frac{{39}}{{360}}$$
Time taken to finish the work by A and B together = $$\frac{{360}}{{39}}$$ = $$\frac{{120}}{{13}}$$ days
98. A pipe can fill a tank in 0.9 hours and another pipe can empty in 0.7 hours. If tank is completely filled and both pipes are opened simultaneously then 450 liters of water is removed from the tank is 2.5 hours. What is the capacity of the tank?
a) 200 liters
b) 350 liters
c) 456 liters
d) 567 liters
Discussion
Explanation: Pipe A can fill the empty tank in = 0.9 hours
So work rate of the Pipe A = $$\frac{{100}}{{0.9}}$$ % per hour
Pipe B can empty the tank in = 0.7 hours
Negative Work rate of B = $$\frac{{100}}{{0.7}}$$ % per hour. (B is removing water, so, taken as negative work)
Tank fill per hour = $$\frac{{100}}{{0.7}} - \frac{{100}}{{0.9}}$$ = 31.75% per hour
Time Taken to empty the tank = $$\frac{{100}}{{31.75}}$$ ≈ 3.15 hours
Capacity of the tank = 3.15 × 180 = 567 liters
99. A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
a) $$\frac{1}{4}$$
b) $$\frac{1}{{10}}$$
c) $$\frac{7}{{15}}$$
d) $$\frac{8}{{15}}$$
Discussion
Explanation:
$$\eqalign{ & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{15}} \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{20}} \cr & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1day's}}\,{\text{work}} \cr & = {\frac{1}{{15}} + \frac{1}{{20}}} = \frac{7}{{60}} \cr & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{4}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{7}{{60}} \times 4} = \frac{7}{{15}} \cr & {\text{Remaining}}\,{\text{work}}\, = {1 - \frac{7}{{15}}} = \frac{8}{{15}} \cr} $$
100. A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
a) $$9\frac{1}{5}$$ days
b) $$9\frac{2}{7}$$ days
c) $$9\frac{3}{5}$$ days
d) 10
Discussion
Explanation:
$$\eqalign{ & \left( {{\text{A + B + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{4} \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{16}} \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{12}} \cr & {\text{C's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \frac{1}{4} - \left( {\frac{1}{{16}} + \frac{1}{{12}}} \right) = {\frac{1}{4} - \frac{7}{{48}}} = \frac{5}{{48}} \cr & {\text{C}}\,\,{\text{alone}}\,{\text{can}}\,{\text{do}}\,{\text{the}}\,{\text{work}}\,{\text{in}} \cr & \frac{{48}}{5} = 9\frac{3}{5}\,{\text{days}} \cr} $$