Description for Correct answer:
During the first 3 minutes all 3 pipes are open. i.e.\( \Large \left(\frac{3}{4}+\frac{3}{8}-\frac{3}{6}\right) \)th = \( \Large \frac{18+9-12}{24}=\frac{15}{24} \)th of the lank will be full.

Then Pipe C is shut. Pipe A and Pipe B will fill \( \Large \frac{1}{4}+\frac{1}{8}=\frac{3}{8} \)th of the tank every minute.

As \( \Large \frac{15}{24} \)th of the tank is already full, Pipes A and B together have to fill

= \( \Large 1 - \frac{15}{24}=\frac{9}{24}=\frac{3}{8} \)th of the tank.

Therefore, it will take another 1 minute, after Pipe C is shut, to fill the tank.