# Moderate Time and Work Solved QuestionAptitude Discussion

 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

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