# Time and work

1.

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
A.

1
4
B.

1
10
C.

7
15
D.

8
15

Explanation:

A’s 1 day’s work =     1     ;
15

B’s 1 day’s work =     1     ;
20

(A + B)’s 1 day’s work =     (     1     +     1     )     =     7     .
15     20     60

(A + B)’s 4 day’s work =     (     7     x 4     )     =     7     .
60     15

Therefore, Remaining work =     (     1 –     7     )     =     8     .
15     15

2.

A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
A.

9     1     days
5
B.

9     2     days
5
C.

9     3     days
5
D.     10

Explanation:

(A + B + C)’s 1 day’s work =     1     ,
4

A’s 1 day’s work =     1     ,
16

B’s 1 day’s work =     1     .
12

Therefore C’s 1 day’s work =     1     –     (     1     +     1     )     =     (     1     –     7     )     =     5     .
4     16     12     4     48     48

So, C alone can do the work in     48     = 9     3     days.
5     5

3.

A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
A.     12 days    B.     15 days
C.     16 days    D.     18 days

Explanation:

A’s 2 day’s work =         1     x 2         =     1     .
20     10

(A + B + C)’s 1 day’s work =         1     +     1     +    1         =     6     =     1     .
20     30     60     60     10

Work done in 3 days =         1     +     1         =     1     .
10     10     5

Now,     1     work is done in 3 days.
5

Whole work will be done in (3 x 5) = 15 days.

4.

A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
A.     20 days    B.
22     1     days
2
C.     25 days    D.     30 days

Explanation:

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 – 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes         3     x 60         = 90 days.
2

So, A takes 30 days to do the work.

A’s 1 day’s work =     1
30

B’s 1 day’s work =     1
90

(A + B)’s 1 day’s work =         1     +     1         =     4     =     2
30     90     90     45

A and B together can do the work in     45     = 22     1     days.
2     2

5.

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
A.     Rs. 375    B.     Rs. 400
C.     Rs. 600    D.     Rs. 800

Explanation:

C’s 1 day’s work =     1     –         1     +     1         =     1     –     7     =     1     .
3     6     8     3     24     24

A’s wages : B’s wages : C’s wages =     1     :     1     :     1     = 4 : 3 : 1.
6     8     24

C’s share (for 3 days) = Rs.         3 x     1     x 3200         = Rs. 400.