# Time and work

11.

A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
A.     5    B.

5     1
2
C.     6    D.     8

Explanation:

B’s 10 day’s work =     (     1     x 10     )     =     2     .
15     3

Remaining work =     (     1 –     2     )     =     1     .
3     3

Now,     1     work is done by A in 1 day.
18

Therefore     1     work is done by A in     (     18 x     1     )     = 6 days.
3     3

12.

4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
A.     35    B.     40
C.     45    D.     50

Explanation:

Let 1 man’s 1 day’s work = x and 1 woman’s 1 day’s work = y.

Then, 4x + 6y =     1     and 3x + 7y =     1     .
8     10

Solving the two equations, we get: x =     11     , y =     1
400     400

1 woman’s 1 day’s work =     1     .
400

10 women’s 1 day’s work =         1     x 10         =     1     .
400     40

Hence, 10 women will complete the work in 40 days.

13.

A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?
A.     40    B.     50
C.     54    D.     60

Explanation:

(A + B)’s 20 day’s work =     (     1     x 20     )     =     2     .
30     3

Remaining work =     (     1 –     2     )     =     1     .
3     3

Now,     1     work is done by A in 20 days.
3

Therefore, the whole work will be done by A in (20 x 3) = 60 days.

14.

P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?
A.
5     5
11
B.
5     6
11
C.
6     5
11
D.
6     6
11

Explanation:

P can complete the work in (12 x 8) hrs. = 96 hrs.

Q can complete the work in (8 x 10) hrs. = 80 hrs.

P’s1 hour’s work =     1     and Q’s 1 hour’s work =     1     .
96     80

(P + Q)’s 1 hour’s work =         1     +     1         =     11     .
96     80     480

So, both P and Q will finish the work in         480         hrs.
11

Number of days of 8 hours each =         480     x     1         =     60     days = 5     5     days.
11     8     11     11