Back out one tap’s rate from joint fill Taps A, B and C together fill an empty cistern in 10 minutes. A alone fills in 30 minutes; B alone fills in 40 minutes. How long would C alone take to fill it?

Introduction / Context:
This is an inverse-rate problem: the total rate equals the sum of individual rates. Given the joint time and two singles, we solve for the third single rate by subtraction.

Given Data / Assumptions:

• All three: 10 min ⇒ rate = 1/10 per minute.
• A: 30 min ⇒ 1/30 per minute.
• B: 40 min ⇒ 1/40 per minute.

Concept / Approach:
Rate(C) = Rate(all) − Rate(A) − Rate(B). Then time(C) = 1 / Rate(C).

Step-by-Step Solution:

Verification / Alternative check:
Check: 1/30 + 1/40 + 1/24 = (4 + 3 + 5)/120 = 12/120 = 1/10.

Why Other Options Are Wrong:
16 and 32 yield wrong sums; 40 is B’s time, not C’s.

Common Pitfalls:
Adding times instead of rates; forgetting to use a common denominator.

Final Answer:
24 min