Multiple choice

A water tank can be filled by pipes P and Q in 4 minutes and 3 minutes, respectively. When the tank is full, it can be emptied by opening a hole in 2 minutes only. If all the taps are turned on at the same time, then the water tank will be filled in

  1. 12 minutes

  2. 6 minutes

  3. 24 minutes

  4. 48 minutes

  5. 1/12 minutes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

P fills 1/4 tank per minute, Q fills 1/3 tank per minute, and the hole empties 1/2 tank per minute. The net rate is (1/4 + 1/3 - 1/2) = (3/12 + 4/12 - 6/12) = 1/12 tank per minute. Thus, the tank fills in 12 minutes.

AI explanation

Using the least common multiple method, let the total capacity of the tank be 12 units. Pipes P and Q fill at rates of 12 / 4 = 3 and 12 / 3 = 4 units per minute, respectively. The hole empties the tank at 12 / 2 = 6 units per minute. The net filling rate with all taps open is 3 + 4 - 6 = 1 unit per minute. Using the formula for time, the tank is filled in 12 / 1 = 12 minutes. The tank will be filled in 12 minutes.

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