Multiple choice

Two pipes can fill a cistern in 12 hours and 15 hours. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 20 minutes extra are taken for the cistern to be filled up. When the cistern is full, in what time will the leak empty it?

  1. 120 hours

  2. 130 hours

  3. 140 hours

  4. 160 hours

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rate of pipes: 1/12 + 1/15 = 9/60 = 3/20. Time to fill = 20/3 hours = 6 hours 40 minutes. With leak, time taken = 6 hours 40 mins + 20 mins = 7 hours. Combined rate with leak = 1/7. Leak rate = 3/20 - 1/7 = (21-20)/140 = 1/140. Thus, the leak empties the cistern in 140 hours.

AI explanation

Using the least common multiple of 12 and 15 as the capacity, the tank is assumed to hold 60 units. The two filling pipes have rates of 5 units and 4 units per hour, giving a combined rate of 9 units per hour, meaning they would normally fill the tank in 60 divided by 9 hours, or 6 hours and 40 minutes. Due to the leak, the filling takes 20 minutes longer, making the actual filling time 7 hours. The effective filling rate with the leak is 60 units divided by 7 hours, equalling 60/7 units per hour. The difference between the normal rate and the effective rate gives the leak's emptying rate: 9 minus 60/7 equals 3/7 units per hour. The time the leak takes to empty the full 60-unit tank is 60 divided by 3/7, resulting in 140 hours.

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