Question

$A,B$ and $C$ can do a piece of work in 20, 30 and 60 days respectively. In how many days can $A$ do the work if he is assisted by $B$ and $C$ on every third day?

• A. $12$ days
• B. $15$ days
• C. $16$ days
• D. $18$ days

Answer 1

Answer: (B)

$15$ days

$A$'s 2 days' work $=2\times \frac{1}{20}=\frac{1}{10}$
$(A+B+C)$'s 1 days' work $=\frac{1}{20}+\frac{1}{30}+\frac{1}{60}=\frac{3+2+1}{60}=\frac{6}{60}=\frac{1}{10}$
Since $A$ is assisted by $B$ and $C$ on every third day.
Work done in 3 days $=\frac{1}{10}+\frac{1}{10}=\frac{1}{5}$
$\frac{1}{5}$ of the work is done in 3 days
$\therefore$ Whole work is done in $3\times \frac{5}{1}=15$ days.