Aptitude 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.**