# Aptitude - Time and Work

### Exercise :: Time and Work - General Questions

21.

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

Explanation:

 Suppose A, B and C take x, x and x days respectively to finish the work. 2 3

 Then, 1 + 2 + 3 = 1 x x x 2 6 = 1 x 2 x = 12.

So, B takes (12/2) = 6 days to finish the work.

22.

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

Explanation:

 (A + B)'s 1 day's work = 1 + 1 = 1 . 15 10 6

 Work done by A and B in 2 days = 1 x 2 = 1 . 6 3

 Remaining work = 1 - 1 = 2 . 3 3

 Now, 1 work is done by A in 1 day. 15 2 work will be done by a in 15 x 2 = 10 days. 3 3

Hence, the total time taken = (10 + 2) = 12 days.

23.

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

Explanation:

 2(A + B + C)'s 1 day's work = 1 + 1 + 1 = 15 = 1 . 30 24 20 120 8

 Therefore, (A + B + C)'s 1 day's work = 1 = 1 . 2 x 8 16

 Work done by A, B, C in 10 days = 10 = 5 . 16 8

 Remaining work = 1 - 5 = 3 . 8 8

 A's 1 day's work = 1 - 1 = 1 . 16 24 48

 Now, 1 work is done by A in 1 day. 48

 So, 3 work will be done by A in 48 x 3 = 18 days. 8 8

24.

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

Explanation:

Ratio of rates of working of A and B = 2 : 1.

So, ratio of times taken = 1 : 2.

 B's 1 day's work = 1 . 12 A's 1 day's work = 1 ; (2 times of B's work) 6

 (A + B)'s 1 day's work = 1 + 1 = 3 = 1 . 6 12 12 4

So, A and B together can finish the work in 4 days.

25.

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

Explanation:

(20 x 16) women can complete the work in 1 day. 1 woman's 1 day's work = 1 . 320

(16 x 15) men can complete the work in 1 day. 1 man's 1 day's work = 1 240

So, required ratio
 = 1 : 1 240 320
 = 1 : 1 3 4
= 4 : 3 (cross multiplied)