Two inlets P and Q can fill a cistern in 12 minutes and 15 minutes, respectively. Both are opened together, but after exactly 3 minutes, P is turned off and only Q continues. How much longer (beyond the first 3 minutes) will it take to fill the cistern completely?

Introduction / Context:
We find the fraction filled in the first 3 minutes with both inlets, then compute the remaining time with only Q running at its solo rate.

Given Data / Assumptions:

• P = 1/12 tank/min.
• Q = 1/15 tank/min.
• Both on for 3 minutes; after that only Q continues.

Concept / Approach:
Phase 1 fill = 3 * (1/12 + 1/15). Remainder / (1/15) gives the additional minutes needed.

Step-by-Step Solution:

Verification / Alternative check:
In 8.25 min, Q adds 8.25/15 = 11/20; total reaches 1.

Why Other Options Are Wrong:
Other times do not correspond to the exact remainder at Q’s rate.

Common Pitfalls:
Arithmetic with common denominators; avoid rounding until the end.

Final Answer:
8 1/4 minutes