Description for Correct answer:
Pipe A fills \( \Large \frac{1}{40} \)th of the tank every minute. Pipe B fills \( \Large \frac{1}{20} \)th every minute. The crack at the bottom drains \( \Large \frac{1}{120} \)th of the tank every minute.

Therefore, when both the pipes are opened and the crack is left unchecked,

\( \Large \frac{1}{40}+\frac{1}{20}=\frac{1}{120} \)th of the tank gets filled.

That is, \( \Large \frac{3+6-1}{120}=\frac{8}{120}=\frac{1}{15} \)th of the tank gets filled every minute.

Hence, the tank will be full in 15 minutes.