# Exercise 1

1) A does a work in 10 days and B does the same work in 15 days. In how many days they together will do the same work ? (R.R.B. 2003)
A) 5 days
B) 6 days
C) 8 days
D) 9 days

Explanation:A can complete a work in 10days.
As 1 day’s works = 1/10
B can complete a work 15days
As 1 day’s works = 1/15
(A+B) both together complete a piece of work
A+B=1/10+1/15=(3+2)/30=5/30=1/6
So, both together will finish the work in 6 days.

2) A can finish a work in 18 days and B can do the same work in half the9 d he time taken by A. Then, working together, what part of the same work they can finish in a day ?
A) 5 days
B) 8 days
C) 6 days
D) 9 days

Explanation: A can finish a work in 18 days.
As 1 day’s works = 1/18
B can finish a work 9 days
As 1 day’s works = 1/9
(A+B) together complete a piece of work
A+B=1/18+1/9=1+2/18=3/18=1/6
So, both complete will finish the work in 6 days.

3) A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in ? (C.B.I 2003)
B) 25/7 days
C) 26/7 days
D) 30/7 days

Explanation:A can complete a work in 24 days
As 1 day’s works = 1/24
B can complete a work in 6 days
As 1 day’s works = 1/6
C can complete a work in 12 days
As 1 day’s works = 1/12
(A+B+C)=1/24+1/6+1/12=(1+4+2)/24=7/24
So, A,B,C together will finish the work in 24/7

4)A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together ? (Hotel Management, 2003)
A) Less than 6 days
B) Exactly 6 days
C) Approximately 6.4 days
D) More than 10 days Man can do a job in 15 days

Explanation:As 1 day’s work=1/15
Father can do a job in 20 days
As 1 day’s work=1/20
Son can do a job in 25 days
As 1 day’s work=1/25
(Man+Father+Son)=(1/15+1/20+1/25)=(20+15+12)/300=47/300
So all the three together will complete the work in 300/47=6.4 days

5)A man can do a piece of work in 5 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ? , (S.S.C. 2004)
A)16/2
B)16
C)15/2
D)20/3

Explanation:(1)A can do this work in 5 days
A and his son together this work in 3 days
His son work = 1/5-1/3=(3-5)/15=2/15
The son alone can do the work in 15/2

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