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?

• A. 100 days
  
• B. 150 days
• C. 60 days
• D. 80 days

Answer 1

The correct option is C 60 days

Work done by (X + Y)’s in one day = $\frac{1}{72}\dots \left(1\right)$
Work done by (Y + Z)’s in one day = $\frac{1}{120}\dots \left(2\right)$
Work done by (Z + X)’s in one day = $\frac{1}{90}\dots \left(3\right)$

(1) + (2) + (3) gives,
$2(X+Y+Z)=\frac{1}{72}+\frac{1}{120}+\frac{1}{90}=\frac{5+3+4}{360}=\frac{12}{360}=\frac{1}{30}$
$\therefore (X+Y+Z{)}^{\prime }s$ one day work $=\frac{1}{2}\times \frac{1}{30}=\frac{1}{60}$
$\therefore$ They will completed the work in 60 days.