Multiple choice

A tank of 3600 m3 capacity is full of water. An outlet pipe is 10 m3/min faster than the inlet pipe and take 12 min less to empty the tank than to fill the tank. Find the rate at which the inlet pipe fills the tank?

  1. 40 m3/min

  2. 45 m3/min

  3. 50 m3/min

  4. 60 m3/min

  5. 65 m3/min
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let inlet rate = x m³/min, then outlet rate = (x+10) m³/min. Time to fill = 3600/x, time to empty = 3600/(x+10). Given 3600/x - 3600/(x+10) = 12. Multiply by x(x+10): 3600(x+10-x) = 12x(x+10), giving 36000 = 12x² + 120x, or x² + 10x - 3000 = 0. This factors to (x+60)(x-50) = 0, so x = 50 (positive rate).

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