Multiple choice

A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water in the tank at the rate of 6 litres per minute. When the tank is full, the inlet pipe is opened and due to the leak, the tank is emptied in 12 hours. How many litres can the cistern hold?

  1. 7960

  2. 7840

  3. 8640

  4. 8290
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let capacity be C. Leak empties at rate C/8. Inlet fills at 6 L/min. Combined rate: (C/8 - 6*60) = C/12. C/8 - C/12 = 360. (3C - 2C)/24 = 360. C = 360 * 24 = 8640.

AI explanation

The inlet pipe fills at 6 litres per minute, which is 360 litres per hour, and over 12 hours it supplies 4320 litres. Because the full tank empties in 12 hours despite this inflow, the leak's emptying rate must equal the inflow rate plus the tank's capacity divided by 12 hours. Using the net work equation, the leak empties at Capacity divided by 8 units per hour, and the net rate is negative Capacity divided by 12 units per hour. Solving the equation (Capacity divided by 8) minus 360 equals (negative Capacity divided by 12) yields a capacity of 8640 litres.

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