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

The correct option is B $15$ days

$A^{\prime }s$ $2$ days work $=(\frac{1}{20}\times 2)=\frac{1}{10}$

$(A+B+C{)}^{\prime }s$ $1$ day work $=(\frac{1}{20}+\frac{1}{30}+\frac{1}{60})=\frac{6}{60}=\frac{1}{10}$

Work done in $3$ days $=(\frac{1}{10}+\frac{1}{10})=\frac{1}{5}$
Now, $\frac{1}{5}$ work is done in $3$ days.
$\therefore$ Whole work will be done in $5\times 3=15$ days