Multiple choice

Two pipes can fill a cistern separately in $24\ min$ and $40\ min$ respectively. Waste pipe is opened which can drain the cistern at $30\ liters/ minute$. If all the pipe are opened together then the cistern fills in one hour. The capacity (in litre) of the cistern is?

  1. $800$
  2. $400$
  3. $600$
  4. $500$

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

Let capacity be C. Pipe A fills at C/24, Pipe B at C/40. Waste pipe drains at 30 L/min. In 60 mins, (C/24 + C/40 - 30) * 60 = C. (5C/120 + 3C/120 - 30) * 60 = C. (8C/120 - 30) * 60 = C. (C/15 - 30) * 60 = C. 4C - 1800 = C. 3C = 1800, C = 600.

AI explanation

Assume the total capacity of the cistern is the least common multiple of 24, 40, and 60, which is 120 units. The rates of the two filling pipes are 5 units per minute and 3 units per minute. With all pipes open, the tank fills in 60 minutes, so the net rate is 120 units per 60 minutes, or 2 units per minute. The equation 5 + 3 - Waste pipe rate = 2 shows the waste pipe drains at 6 units per minute. Because the actual waste pipe drains 30 liters per minute, the scaling factor is 5, making the total capacity 120 multiplied by 5, which is 600 liters.

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