Two pipes P and Q can fill a tank in 45 minutes and 60 minutes respectively. Both pipes are opened together for some time and then pipe P is turned off. If the tank is filled in 28 minutes, then the time for which pipe P worked is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 24 minutes
In one minute P fills \( \frac{1}{45} \) of the tank and Q fills \( \frac{1}{60} \). Q runs for all 28 minutes; let P run for t minutes.
\( \displaystyle \frac{t}{45}+\frac{28}{60}=1 \)
\( \displaystyle \frac{t}{45}=1-\frac{7}{15}=\frac{8}{15} \)
\( \displaystyle t=\frac{8}{15}\times 45=24 \)
So P worked for 24 minutes.