Question

$P,$ $Q$ and $R$ can do a piece of work in $10,$ $20$ and $30$ days respectively. In how many days can $Q$ do the work if he is assisted by $P$ and $R$ on every fourth day?

• A. $10$ days
• B. $12$ days
• C. $14$ days
• D. $16$ days

Answer 1

The correct option is B $12$ days

$Q^{\prime }s$ $3$ days work $=(\frac{1}{20}\times 3)=\frac{3}{20}$

$(P+Q+R{)}^{\prime }s$ $1$ day work $=(\frac{1}{10}+\frac{1}{20}+\frac{1}{30})=\frac{11}{60}$

Work done in $4$ days $=(\frac{3}{20}+\frac{11}{60})=\frac{20}{60}=\frac{1}{3}$
Now, $\frac{1}{3}$ work is done in $4$ days.
$\therefore$ Whole work will be done in $4\times 3=12$ days