1. 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
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)
$$\eqalign{ & x = 15, \cr & y = 18,{\text{ }} \cr & z = 21 \cr} $$
2. 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
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
$$\eqalign{ & {\text{ = }}\left( {100 \times \frac{3}{{40}}} \right){\text{hours}} \cr & = 8\frac{1}{4}{\text{hours}} \cr & = {\text{8 hours 15 minutes}} \cr} $$
3. 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) $$\frac{{20000{\text{r}}}}{{60{\text{pq}}}}$$
Explanation: Length of the cloth produced in 1 hour
$$\eqalign{ & {\text{ = }}\left( {\frac{{{\text{pq}}}}{{\text{r}}} \times 60} \right){\text{ m }} \cr & = \left( {\frac{{60{\text{pq}}}}{{\text{r}}}} \right){\text{ m}} \cr & {\text{Required time}} \cr & = \left( {20000 \div \frac{{60{\text{pq}}}}{{\text{r}}}} \right){\text{ hours }} \cr & {\text{ = }}\left( {\frac{{20000{\text{r}}}}{{60{\text{pq}}}}} \right){\text{ hours}} \cr} $$
4. 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
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
$$\eqalign{ & \frac{{11}}{6}{\text{man can complete a work in}} \cr & = \frac{{88}}{{\frac{{11}}{6}}}\, = 48{\text{ days }} \cr} $$
5. 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
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
6. 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.
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
7. 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
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
8. 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
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
9. 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
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
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) 7.5 hr
b) 8 hr
c) 8.5 hr
d) 10 hr
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.