## Time and Work Questions and Answers Part-1

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

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%

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 From second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in 55% of the time.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

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

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

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

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

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

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

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

$$\Rightarrow \frac{1}{{10}} + \frac{1}{{12}} - \frac{1}{{20}} = \frac{2}{{15}}$$
Hence, tank will be filled in $$\frac{{15}}{2}$$ = 7.5 hour.