A cistern has two inlet taps that fill it in 12 minutes and 15 minutes, respectively. There is also a waste pipe (outlet). When all three pipes are opened together on an empty cistern, it becomes full in 20 minutes. How long does the waste pipe alone take to empty a full cistern?

Introduction / Context:
Combine inlet rates and subtract the unknown outlet rate to match the observed net fill time. Then invert the outlet rate to get its emptying time for a full cistern.

Given Data / Assumptions:

• Inlet A = 1/12 tank/min.
• Inlet B = 1/15 tank/min.
• All three together fill in 20 min ⇒ net rate = 1/20 tank/min.

Concept / Approach:
If w is the outlet rate (tank/min), then 1/12 + 1/15 − w = 1/20. Solve for w, then time = 1/w.

Step-by-Step Solution:

Verification / Alternative check:
Net with all = 3/20 − 1/10 = 3/20 − 2/20 = 1/20, consistent.

Why Other Options Are Wrong:
8/12/16 min imply different net rates and would not yield 20 minutes to fill.

Common Pitfalls:
Adding the outlet by mistake; always subtract outlets.

Final Answer:
10 min