Multiple choice

A tank can be filled by three pipes in 20 min, 30 min and 60 min, respectively. When the tank is empty, the three pipes are opened. After 4 min, the first pipe stops working. After how much time will the 2nd and 3rd pipes fill the tank?

  1. 6 min

  2. 8 min

  3. 10 min

  4. 12 min

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

The pipes fill 1/20, 1/30, and 1/60 of the tank per minute. In 4 minutes, the three pipes together fill 4 * (1/20 + 1/30 + 1/60) = 4 * (3+2+1)/60 = 4 * 6/60 = 2/5 of the tank. The remaining 3/5 of the tank is filled by the 2nd and 3rd pipes at a combined rate of (1/30 + 1/60) = 3/60 = 1/20 per minute, taking (3/5) / (1/20) = 12 minutes.

AI explanation

In the first 4 minutes, all three pipes work together at a combined rate of 1/20 + 1/30 + 1/60 per minute. This gives a rate of 6/60 or 1/10 of the tank per minute, so in 4 minutes they fill 4/10 or 2/5 of the tank. The remaining work is 1 minus 2/5, which equals 3/5 of the tank. The combined rate of the 2nd and 3rd pipes is 1/30 + 1/60, which equals 3/60 or 1/20 per minute. The additional time needed is the remaining work divided by their rate, so (3/5) divided by (1/20) equals 12 minutes.

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