Description for Correct answer:
Part filled by pipe P in 1 min = \( \Large \frac{1}{12} \)

Part filled by pipe Q in 1 min = \( \Large \frac{1}{15} \)

Part filled by both pipes in 1 min

= \( \Large \frac{1}{12} \)+ \( \Large \frac{1}{15} \)= \( \Large \frac{5+4}{60} \)= \( \Large \frac{9}{60} \)

Now, part filled by both pipes in 3 min

= \( \Large \frac{3 \times 9}{60}=\frac{27}{60}=\frac{9}{20} \)

Remaining part = \( \Large 1 - \frac{9}{20} = \frac{11}{20} \)

Let the remaining part is filled by pipe Q in x min.

Then, \( \Large x \times \frac{1}{15} = \frac{11}{20} \)

\( \Large x = \frac{15 \times 11}{20} = \frac{3 \times 11}{4}

= \frac{33}{4} = 8\frac{1}{4} min \)