Aptitude - Time and Work

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

Answer: Option B

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

Answer: Option C

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

Therefore 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

Answer: Option A

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

Answer: Option A

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

Therefore 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

Answer: Option B

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)