Two pipes A and B can fill a tank respectively in 30 min and 45 min. Both A and B are opened together for some time and then pipe B is turned off. If the tank is filled in 20 min, then find after how many minutes the pipe B is turned off?

15 min

The correct answer is Option (3) → 15 min

Let the tank capacity be 1 unit.

Filling rates:

Pipe A: $\frac{1}{30}$ per min

Pipe B: $\frac{1}{45}$ per min

Let pipe B be turned off after $t$ minutes. Both A and B run together for $t$ minutes, then only A runs for remaining $(20 - t)$ minutes.

Total filled:

$t\left(\frac{1}{30} + \frac{1}{45}\right) + (20 - t)\left(\frac{1}{30}\right) = 1$

Compute combined rate: $\frac{1}{30} + \frac{1}{45} = \frac{3+2}{90} = \frac{5}{90} = \frac{1}{18}$

Equation:

$t \cdot \frac{1}{18} + (20 - t) \cdot \frac{1}{30} = 1$

$\frac{t}{18} + \frac{20 - t}{30} = 1$

Multiply through by 90:

$5t + 3(20 - t) = 90$

$5t + 60 - 3t = 90 \Rightarrow 2t + 60 = 90 \Rightarrow 2t = 30 \Rightarrow t = 15$