Exercise : 2


1. A water tank has three taps A, B and C. Tap A, when opened,can fill the water tank alone in 4 hours. Tap B, when opened, can fill the water tank alone in 6 hours and tap C, when opened, can empty the water tank alone in 3 hours. If taps A, B and C are opened simultaneously, how long will it take to fill the tank completely?
(a) 10 hours
(b) 8 hours
(c) 18 hours
(d) 12 hours
(e) None of these
Ans.d

Required time to fill the tank

= \(\frac{1}{\left(\frac{1}{4} + \frac{1}{6} \right) - \frac{1}{3}} = \frac{1}{\frac{5}{12} - \frac{1}{3}} = \frac{1}{\frac{1}{12}} = 12 h\)

2. Twenty-four men can complete a work in sixteen days. Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working and worked for twelve days. How many more men are to be added to complete the remaining work in 2 days?
(a) 48
(b) 24
(c) 36
(d) 16
(e) None of the above
Ans.b

24 men complete the work in 16 days

∴ 16 men complete (1624 × 1216) = 12 part of work in 12 days

32 women complete the work in 24 days

∴ 16 women complete 1632 × 1424) = 724 part of work in (12 + 2 ) = 14 days

So, the remaining part of the work which is done by sixteen men + sixteen women and the reqd additional no. of men in 2 days

= 1 - (12 + 724) = 12 - 724 = 524 (part)

Now, in 2 days 524 part of the work is done by

24 × 162 × 524 = 40 men

Hence, the reqd. additional no. of men

= 40 – 16 = 24 men.

3. The total monthly income of four men and two women is 46,000. If every woman earns 500 more than a man then what is the monthly income of a woman?
(a) 7,500
(b) 8,000
(c) 9,000
(d) 6,500
(e) None of these
Ans.b

4M + 2W = 46000;

Again, W = M + 500

or, M = W – 500

∴ (W – 500) + 2W = 46000

or, 6W = 46000 + 2000 = 48000

∴ W = 8000

4. 10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will the work get completed?
(a) 6
(b) 723
(c) 623
(d) 613
(e) None of these
Ans.c

10 men + 15 women in 1 day do 115 + 112 = 960 work

\ Time taken = 609 days = 623 days

5. ‘A’ completes a work in 12 days. ‘B’ completes the same work in 15 days. ‘A’ started working alone and after 3 days B joined him. How many days will they now take together to complete the remaining work?
(a) 5
(b) 8
(c) 6
(d) 4
(e) None of these
Ans.a

Work done by ‘A’ in 3 days

= 112 × 3 = 14

∴ Remaining work = 1 - 14 = 34

Work done by A and B together = \(\frac{12 \times 15}{27} = \frac{20}{3}\)

∴ Remaining work done by A and B together in

= 34 × 203 = 5 days

6. Rajani has to read a book of 445 pages. She has already read the first 157 pages of the book and if she reads 24 pages of the book everyday then how long will she take now to complete the book?
(a) 25 days
(b) 20 days
(c) 46 days
(d) 21 days
(e) None of these
Ans.e

Remaining pages to read = 445 – 157 = 288

∴ Reqd. number of days = 28824 = 12

7. 24 men working 8 hours a day can finish a work in 10 days. Working at the rate of 10 hours a day, the number of men required to finish the same work in 6 days is
(a) 30
(b) 36
(c) 34
(d) 32
(e) None of these
Ans.d

m1 × d1 × t1 × w2 = m2 × d2 × t2 × w1

24 × 10 × 8 × 1 = m2 × 6 × 10 × 1

⇒ m2 = \(\frac{24 \times 10 \times 8}{6 \times 10}\) = 32 men

8. X and Y can do job in 25 days and 30 days respectively. They work together for 5 days and then X leaves. Y will finish the rest of the work in how many days?
(a) 18 days
(b) 19 days
(c) 20 days
(d) 21 days
(e) None of these
Ans.b

X’s one day’s work = 1.25 th part of whole work.

Y’s one day’s work = 130 th part of whole work.

Their one day’s work = 125 + 130 = 1150 th part of whole work.

Now, work is done in 5 days = 11150 × 5 = 1130 th of whole work

∴ Remaining work = 1 - 1130 = 1930 th of whole work

Now, 130 th work is done by Y in one day.

1930 th work is done by Y in \(\frac{1}{\frac{1}{30}} \times \frac{19}{30}\) = 19 days.

9. A and B can do a job is 16 days and 12 days respectively. 4 days before finishing the job, A joins B. B has started the work alone. Find how many days B has worked alone?
(a) 6 days
(b) 4 days
(c) 5 days
(d) 7 days
(e) None of these
Ans.c

A’s one day’s work = 116 th work

B’s one day’s work 112 th work

Let B has worked alone = x days. Then,

A’s amount of work + B’s amount of work = 1

⇒ 4(116) + (x + 4)(112) = 1

\(\frac{1}{4} + \frac{x + 4}{12}\) = 1 ⇒ x = 34 × 12 - 4

⇒ x = 5 days.

10. A contractor undertakes to built a walls in 50 days. He employs 50 peoples for the same. However after 25 days he finds that only 40% of the work is complete. How many more man need to be employed to complete the work in time?
(a) 25
(b) 30
(c) 35
(d) 20
(e) None of these
Ans.a

50 men complete 0.4 work in 25 days.

Applying the work rule, m1 × d1 × w2 = m2 × d2 × w1

we have,

50 × 25 × 0.6 = m2 × 25 × 0.4

or m2 = \(\frac{50 \times 25 \times 0.6}{25 \times 0.4}\) = 75 men