Multiple choice

There are two inlet pipes and an outlet pipe. The efficiency of one of the inlet pipes is double than that of the other inlet pipe. The efficiency of the outlet pipe is half that of the lesser-efficient inlet pipe. The empty tank gets filled in 12 h when all the pipes are opened. How many hours will it take to fill the empty tank when the lesser-efficient inlet pipe is plugged and the rest kept opened?

  1. 25 h

  2. 20 h

  3. 15 h

  4. 12 h
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let efficiency of lesser inlet be x, greater be 2x, outlet be x/2. Net efficiency = x + 2x - x/2 = 2.5x. Tank capacity = 2.5x * 12 = 30x. If lesser inlet is plugged, net efficiency = 2x - x/2 = 1.5x. Time = 30x / 1.5x = 20 hours.

AI explanation

Let the efficiency of the lesser-efficient inlet pipe be 2 units per hour, making the other inlet pipe 4 units per hour. The outlet pipe has half the efficiency of the lesser inlet pipe, so its rate is 1 unit per hour. When all are open, the net filling rate is 2 + 4 - 1 = 5 units per hour, meaning the tank's capacity is 5 units per hour multiplied by 12 hours, or 60 units. When the lesser-efficient inlet pipe is plugged, the net rate becomes 4 - 1 = 3 units per hour. Dividing the total capacity of 60 units by this new net rate of 3 units per hour results in 20 hours.

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