Question

Three taps $P,$ $Q$ and $R$ can fill a drum in $10,20$ and $30$ hours respectively. If $P$ is open all the time and $Q$ and $R$ are open for one hour each alternately, then the drum will be full in

• A. $6$ hours
• B. $6.5$ hours
• C. $7$ hours
• D. $7.5$ hours

Answer 1

The correct option is C $7$ hours

Drum filled by both $P$ and $Q$ in $1$ hour $=\frac{1}{10}+\frac{1}{20}=\frac{3}{20}$
Drum filled by both $P$ and $R$ in $1$ hour $=\frac{1}{10}+\frac{1}{30}=\frac{2}{15}$
Drum filled in first $2$ hours $=\frac{3}{20}+\frac{2}{15}=\frac{17}{60}$
So, drum filled in $6$ hours $=3\times \frac{17}{60}=\frac{17}{20}$
$\therefore$ Remaining part $=1-\frac{17}{20}=\frac{3}{20}$
Now, it is the turn of $P$ and $Q$ and $\frac{3}{20}$ part is filled by $P$ and $Q$ in $1$ hour.
Therefore, total time taken to fill the drum $=(6+1)=7$ hours