Question

X and Y can do a piece of work in 72 days. Y and Z can do it in 120 days. X and Z can do it in 90 days. How many days does it take if all the three can work together?

Answer 1

Work done by X and Y in one day = $\frac{1}{72}\dots \left(1\right)$
Work done by Y and Z in one day = $\frac{1}{120}\dots \left(2\right)$
Work done by Z and X in one day = $\frac{1}{90}\dots \left(3\right)$
(1) + (2) + (3) gives,
$2(X+Y+Z)=\frac{1}{72}+\frac{1}{120}+\frac{1}{90}⟹2(X+Y+Z)=\frac{5+3+4}{360}=\frac{12}{360}=\frac{1}{30}$
$\therefore$ Work done by A, B and C together in one day work $=\frac{1}{2}\times \frac{1}{30}=\frac{1}{60}$
$\therefore$ A, B and C will together complete the work in 60 days.