Question

Three taps A, B, and C together can fill an empty cistern in 10 minutes, tap A alone can fill it in 20 minutes and tap B alone in 40 minutes. How long will tap C alone take to fill it?

• A. 40 minutes
• B. 24 minutes
• C. 32 minutes
• D. 16 minutes

Hint:

Use 40 as a common denominator to make the fraction subtraction easy.

Answer 1

The Correct Option is A

Step 1: Concept
Work rate is additive: $1/T_{total} = 1/T_A + 1/T_B + 1/T_C$.

Step 2: Meaning
Rates: Combined = 1/10, A = 1/20, B = 1/40.

Step 3: Analysis
$1/10 = 1/20 + 1/40 + 1/T_C$. Solving for $1/T_C$: $1/T_C = 1/10 - (1/20 + 1/40) = 4/40 - (2/40 + 1/40) = 4/40 - 3/40 = 1/40$.

Step 4: Conclusion
$T_C = 40$ minutes. Final Answer: (A)