Two pipes can fill a cistern in 30 minutes and 40 minutes, respectively. Both pipes are opened together, but after some time the first pipe is shut off. The cistern is filled in 10 minutes more (by the second pipe alone after the shutdown). How long after the start was the first pipe shut off?
Aptitude
Pipes and Cistern
Difficulty: Medium
Choose an option
Answer
Correct Answer: 90/7 minutes
Explanation
Introduction / Context:Let x be the number of minutes both pipes run. After that, only the second pipe runs for 10 minutes and the tank becomes full. Set up the total work equation and solve for x, the shutdown time of the first pipe.
Given Data / Assumptions:
- Pipe 1 = 1/30 tank/min.
- Pipe 2 = 1/40 tank/min.
- After shutting Pipe 1, Pipe 2 runs 10 additional minutes.
Concept / Approach:Work equation: x*(1/30 + 1/40) + 10*(1/40) = 1. Solve for x in minutes.
Step-by-Step Solution:
1/30 + 1/40 = 7/120.x*(7/120) + 10*(1/40) = 1 ⇒ x*(7/120) + 1/4 = 1.x*(7/120) = 3/4 ⇒ x = (3/4) * (120/7) = 90/7 minutes.Verification / Alternative check:Check totals: (90/7)*(7/120) = 3/4, plus 1/4 from the last 10 minutes equals 1 tank.
Why Other Options Are Wrong:90/11, 90/13, 22.5 are not equal to 12 6/7 minutes.
Common Pitfalls:Misreading “10 minutes more” as total time instead of the post-shutdown segment duration.
Final Answer:90/7 minutes