# Difficult Time and Work Solved QuestionAptitude Discussion

 Q. $X$ alone can do a piece of work in 15 days and $Y$ alone can do it in 10 days. $X$ and $Y$ undertook to do it for Rs. 720. With the help of $Z$ they finished it in 5 days. How much is paid to $Z$?
 ✖ A. Rs. 360 ✔ B. Rs. 120 ✖ C. Rs. 240 ✖ D. Rs. 300

Solution:
Option(B) is correct

In one day $X$ can finish $\dfrac{1}{15}^{th}$of the work.

In one day $Y$ can finish $\dfrac{1}{10}^{th}$of the work.

Let us say that in one day $Z$ can finish $\dfrac{1}{Z}^{th}$ of the work.

When all the three work together in one day they can finish:

$\dfrac{1}{15}+\dfrac{1}{10}+\dfrac{1}{Z}=\dfrac{1}{5}^{th}$

Therefore,

$\dfrac{1}{Z}=\dfrac{1}{30}$

Ratio of their efficiencies

$=\dfrac{1}{15}:\dfrac{1}{10}:\dfrac{1}{30}$

$2:3:1$

Therefore $Z$ receives $\dfrac{1}{6}^{th}$of the total money.

According to their efficiencies money is divided as $240:360:120$.

Hence, the share of $Z$ = Rs. 120.