# 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

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

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

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

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

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)