Two pipes A and B can fill a tank in 20 minutes and 10 minutes respectively. Both pipes A and B are opened together for some time and then pipe B is turned off. If the tank is filled in 15 minutes, then find after how many minutes pipe B is turned off?

2.5 minutes

The correct answer is Option (2) → 2.5 minutes

Let total time tank is filled = 15 min

Let pipe B be turned off after t minutes, then pipe A alone works for remaining (15 - t) minutes

Rates of filling:

Pipe A: $1/20$ tank per minute

Pipe B: $1/10$ tank per minute

Equation for total tank filled:

$\text{A+B working together for t min} + \text{A alone for (15-t) min} = 1$

$t\left(\frac{1}{20} + \frac{1}{10}\right) + (15 - t)\frac{1}{20} = 1$

Simplify:

$t\left(\frac{1 + 2}{20}\right) + \frac{15 - t}{20} = 1$

$t \cdot \frac{3}{20} + \frac{15 - t}{20} = 1$

$\frac{3t + 15 - t}{20} = 1 \Rightarrow \frac{2t + 15}{20} = 1$

$2t + 15 = 20 \Rightarrow 2t = 5 \Rightarrow t = 2.5$

Pipe B is turned off after 2.5 minutes