Multiple choice

Three pipes A, B and C are attached to a tank. A and B can fill it in 20 and 30 minutes, respectively, while C can empty it in 15 minutes. If A, B and C are kept open successively for 1 minute each, how soon will the tank be filled if pipe A is opened first?

  1. 167 minutes

  2. 160 minutes

  3. 157 minutes

  4. 155 minutes

  5. 172 minutes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A fills 1/20, B fills 1/30, C empties 1/15. Net rate per 3 minutes = 1/20 + 1/30 - 1/15 = 3/60 + 2/60 - 4/60 = 1/60. The tank fills 1/60 every 3 minutes. To avoid overfilling, consider the last cycle. After 164 minutes (approx), the tank is near full. Following the sequence, it fills at 167 minutes.

AI explanation

Assume the capacity of the tank is the least common multiple of 20, 30 and 15, which is 60 units. The filling rates for pipes A, B and C are 3 units per minute, 2 units per minute and a removal of 4 units per minute, respectively. In a 3 minute cycle, the net work done is 3 plus 2 minus 4, which equals 1 unit. After 165 minutes, or 55 such cycles, 55 units of the tank are filled, leaving 5 units to be filled. In the next two minutes, pipe A fills 3 units and pipe B fills 2 units, completing the tank. The total time taken is 165 plus 2, resulting in 167 minutes.

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