Time and Work

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$X$ 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 $Z$?


Rs. 360


Rs. 120


Rs. 240


Rs. 300

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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:




Ratio of their efficiencies



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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