If three men A, B and C can complete a work in $P$, $Q$ and $R$ days respectively while working alone, then the number of days they take working together is
A$\dfrac{P+Q+R}{3}$
B$\dfrac{PQR}{PQ+QR+PR}$
C$\dfrac{PQ+QR+PR}{PQR}$
D$\dfrac{PR}{P+Q+R}$
Answer & Solution
Correct answer: B. $\dfrac{PQR}{PQ+QR+PR}$
Their one-day work rates are $1/P$, $1/Q$, and $1/R$. So together their daily work is $\frac{1}{P}+\frac{1}{Q}+\frac{1}{R}=\frac{PQ+QR+PR}{PQR}$. Hence time taken for one whole work is the reciprocal, $\frac{PQR}{PQ+QR+PR}$.
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