Question : X can do a piece of work in $p$ days and Y can do the same work in $q$ days. Then the number of days in which X and Y can together do that work is:
Option 1: $\frac{p+q}{2}$
Option 2: $\frac{1}{p}$ + $\frac{1}{q}$
Option 3: $\frac{pq}{p+q}$
Option 4: $pq$
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Correct Answer: $\frac{pq}{p+q}$
Solution :
Given:
X can do a piece of work in $p$ days and Y can do the same work in $q$ days.
X can do a piece of work in $p$ days ⇒ X in 1 day can do $\frac{1}{p}$ part of the work
and Y can do a piece of work in $q$ days ⇒ Y in 1 day can do $\frac{1}{q}$ part of the work
So, X and Y together in 1 day can do ($\frac{1}{p}$ + $\frac{1}{q}$) = $\frac{q + p}{pq}$ part of the work
Therefore, X and Y can together do that work in (1 ÷ $\frac{q+p}{pq}$) = $\frac{pq}{p+q}$ days.
Hence, the correct answer is $\frac{pq}{p+q}$ days.
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