Question

$A,B$ and $C$ can do a piece of work in 11 days, 20 days, and 55 days respectively working alone. How soon can the work be done if $A$ is assisted by $B$ and $C$ on alternate days?

• A. 7 days
• B. 8 days
• C. 9 days
• D. 10 days

Answer 1

The correct option is B 8 days

$(A+B)$'s 1 day's work $=\left(\frac{1}{11}+\frac{1}{20}\right)=\frac{20+11}{220}=\frac{31}{220}$
$(A+C)$'s 1 day's work $=\left(\frac{1}{11}+\frac{1}{55}\right)=\frac{6}{55}$
$\therefore$ Work done in 2 days $=\frac{31}{220}+\frac{6}{55}=\frac{55}{220}=\frac{1}{4}$
$\frac{1}{4}$th of the work is done in 2 days
$\therefore$ Whole work is done in 8 days.