Multiple choice

Two pipes X and Y can fill an empty tank in 16 and 24 hours respectively. Ravi opens these two pipes simultaneously. After 8/3 hours he comes back and sees that there was a leak in the tank. He stops the leakage and thus tank took 48/5 hours to be filled completely after closing the leak. In what time leakage will empty the filled tank?

  1. 6.9 hrs

  2. 9.6 hrs

  3. 8.4 hrs

  4. 9.4 hrs
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The combined filling rate of pipes X and Y is 1/16 + 1/24 = 5/48 of the tank per hour. After the leak is closed, the tank takes 48/5 hours to fill completely, which means X and Y filled (5/48) * (48/5) = 1 (the entire tank) during this time. This implies that no water accumulated during the first 8/3 hours because the leak rate was exactly equal to the combined filling rate of 5/48. Thus, the leak alone can empty the full tank in 1 / (5/48) = 9.6 hours.

AI explanation

Assume the total capacity is the least common multiple of 16 and 24, which is 48 units. The filling rates for pipes X and Y are 3 and 2 units per hour, giving a combined rate of 5 units per hour. In 8/3 hours, they fill 40/3 units, leaving 104/3 units to be filled. After the leak is closed, pipes X and Y fill the remaining 104/3 units at their normal rate of 5 units per hour, taking 104/15 hours. Since the total filling time after closing the leak is 48/5 hours, the leak wasted 48/5 - 104/15 = 40/15 = 8/3 hours of time. In that wasted time, the leak would have emptied 8/3 hours multiplied by 5 units per hour, which is 40/3 units. The leak rate is the 40/3 units divided by the 8/3 hours it operated, resulting in 5 units per hour. The time taken by the leakage alone to empty the 48-unit tank is 48 divided by 5, which is 9.6 hours.

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