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There are 2 taps connected to a bucket. One tap flow hot water and other tap flow cold water. Hot water tap can fill the bucket in 15 min and cold water tap can fill the bucket in 10 min. A person opened both the tap and left the place. He returned at the time when bucket should be full but he found that due to leakage in the bottom of bucket. It is yet to be full. He reported the leakage and bucket become full in 2 minutes more, in how much time leakage can empty the bucket alone?

There are 2 taps connected to a bucket. One tap flow hot water and other tap flow cold water. Hot water tap can fill the bucket in 15 min and cold water tap can fill the bucket in 10 min. A person opened both the tap and left the place. He returned at the time when bucket should be full but he found that due to leakage in the bottom of bucket. It is yet to be full. He reported the leakage and bucket become full in 2 minutes more, in how much time leakage can empty the bucket alone? Correct Answer 18 min

Let the capacity of bucket be 30.

(∵ LCM of 15 and 30 is 30.)

Efficiency of hot water taps = 30/15 = 2

Efficiency of cold water taps = 30/10 = 3

If bucket has no leakage then time taken to fill bucket = 30/(3 + 2) = 6 min

In 6 min, water empty by leakage = (3 + 2) × 2 = 10

Efficiency of leakage = 10/6 = 5/3

Time taken by leakage to empty the bucket = 30 × 3/5 = 18 min

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