Time and Work
Aptitude

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Q.

Two workers $A$ and $B$ manufactured a batch of identical parts. $A$ worked for 2 hours and $B$ worked for 5 hours and they completed half the job. Then they worked together for another 3 hours and they had to do (1/20)th of the job. How many hours time does $B$ take to complete the job, if he worked alone?

 A.

24

 B.

12

 C.

15

 D.

30

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Solution:
Option(C) is correct

Let '$a$' hours be the time that worker $A$ will take to complete the job. 

Let '$b$' hours be the time that worker $B$ takes to complete the job. 

When $A$ works for 2 hours and $B$ works for 5 hours half the job is done. 

\(\dfrac{2}{a}+\dfrac{5}{b}=\dfrac{1}{2}\).......(1)

When they work together for the next three hours, \(\left(\dfrac{1}{20}\right)^{th}\) of the job is yet to be completed.

They have completed half the job earlier and \(\left(\dfrac{1}{20}\right)^{th}\) is still left.

So by working for 3 hours, they have completed \(1-\dfrac{1}{2}-\dfrac{1}{20}=\dfrac{9}{20}\) of the job

Therefore,

\(\dfrac{3}{a}+\dfrac{3}{b}=\dfrac{9}{20}\)-------(2)

Solving equations (1) and (2), we get $b$ = 15 hours


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