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 then pipe B is turned off. If the tank is filled in 15 minutes, then time for which the pipe B works is:

$7\frac{1}{2}$ minutes

The correct answer is Option (2) → $7\frac{1}{2}$ minutes **

Let $t$ be the time (in minutes) for which pipe B works.

Total filled: $\left(\frac{1}{20}+\frac{1}{30}\right)t+\frac{1}{20}(15-t)=1$

Simplify: $\frac{1}{12}t+\frac{15}{20}-\frac{1}{20}t=1$

Thus $\left(\frac{1}{12}-\frac{1}{20}\right)t=\frac{1}{4}\Rightarrow\frac{1}{30}t=\frac{1}{4}$

$t=\frac{30}{4}=7.5$ minutes

Answer: $7.5\ \text{minutes}\;(7\ \text{minutes }30\ \text{seconds})$