Multiple choice

Rohit purchased a cistern which had a leakage. The cistern can be filled by two inlet pipes, which can individually fill the cistern in 12 min and 15 min, respectively. Despite leakage, the two inlet pipes together can fill the cistern in 20 min. How long will it take to empty the completely full cistern due to leakage?

  1. 10 min.

  2. 12 min.

  3. 15 min.

  4. 16 min.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Inlet 1 rate = 1/12, Inlet 2 rate = 1/15. Combined inlet rate = 1/12 + 1/15 = 5/60 + 4/60 = 9/60 = 3/20. With leakage, rate = 1/20. Leakage rate = Combined inlet rate - Net rate = 3/20 - 1/20 = 2/20 = 1/10. Time to empty = 10 min.

AI explanation

Using the net work equation, let the leak empty the cistern in L minutes. The sum of the individual filling rates of the two pipes minus the leaking rate equals their combined rate: 1 over 12 plus 1 over 15 minus 1 over L equals 1 over 20. Finding a common denominator for the left side gives 9 over 60 minus 1 over L equals 3 over 60. Solving this equation gives 1 over L equals 1 over 10, so the time taken to empty the cistern is 10 min.

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