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?
Aptitude
Pipes and Cistern
Difficulty: Easy
Choose an option
Answer
Correct Answer: 24 min
Explanation
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:
Rate(all) = 1/10 = 12/120Rate(A) + Rate(B) = 1/30 + 1/40 = 4/120 + 3/120 = 7/120Rate(C) = 12/120 − 7/120 = 5/120 = 1/24Time(C) = 24 minVerification / 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