Two pipes P and Q can fill a tank in 26 minutes and 52 minutes respectively. Both the pipes are opened together for some time and then pipe P is closed. If the tank is filled in 26 minutes, then after how many minutes pipe P is closed?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 13 minutes
$\text{Rate of P}=\frac{1}{26},\quad \text{Rate of Q}=\frac{1}{52}$
$\text{Both work for } x \text{ minutes}$
$\text{Work done by both in } x \text{ minutes}=x\left(\frac{1}{26}+\frac{1}{52}\right)=x\left(\frac{3}{52}\right)$
$\text{Remaining time}=26-x$
$\text{Work done by Q alone}=\frac{26-x}{52}$
$x\left(\frac{3}{52}\right)+\frac{26-x}{52}=1$
$\frac{3x+26-x}{52}=1$
$\frac{2x+26}{52}=1$
$2x+26=52$
$2x=26$
$x=13$
Pipe P is closed after $13$ minutes.