Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. Both pipes A and B are opened together for some time and pipe B is turned off. If the tank is filled in 15 minutes, then after how many minutes pipe B is turned off?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 7.5 minutes
Let the total time to fill the tank = 15 min
Let pipe B be turned off after $t$ minutes
Filling rates:
Pipe A: $\frac{1}{20}$ tank/min
Pipe B: $\frac{1}{30}$ tank/min
Equation for total work done:
$\text{Work by A and B together for t minutes} + \text{Work by A alone for (15 - t) minutes} = 1$
$\left(\frac{1}{20} + \frac{1}{30}\right) t + \frac{1}{20} (15 - t) = 1$
$\left(\frac{3 + 2}{60}\right) t + \frac{15 - t}{20} = 1 \Rightarrow \frac{5t}{60} + \frac{15 - t}{20} = 1$
$\frac{t}{12} + \frac{15 - t}{20} = 1$
LCM = 60: $5t + 3(15 - t) = 60 \Rightarrow 5t + 45 - 3t = 60 \Rightarrow 2t = 15 \Rightarrow t = 7.5$ min
Answer: Pipe B is turned off after 7.5 minutes