Description for Correct answer:
According to the question,

Double the 2.5 min = 5 min

Now, part filled in 5 min

= \( \Large 5 \times \left(\frac{1}{12}+\frac{1}{15}\right) = 5 \times \left(\frac{5+4}{60}\right) \)

= \( \Large 5 \times \frac{9}{60} = \frac{3}{4} \)

Part emptied in 1 min when R R and all are opened.

= \( \Large \frac{1}{6}- \left(\frac{1}{12}+\frac{1}{15}\right)=\frac{1}{6}- \left(\frac{5+4}{60}\right) \)

=\( \Large \left(\frac{1}{6}-\frac{3}{2}\right)=\frac{1}{60} \)

One-sixtieth part is emptied in 1 min.

Therefore, Three-fourth part will be emptied in\( \Large 60 \times \frac{3}{4}=15 \times 3 \) = 45 min.