Time and Work
Aptitude

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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

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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.


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