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Two pipe A and B can fill a water tank in 20 and 24 minutes respectively and a third pipe C can empty at the rate of 3 gallons per minute. If A, B and C are open together to fill the tank in 15 minutes, find the capacity of tank?

a) 180 gallons
b) 150 gallons
c) 120 gallons
d) 60 gallons

Answer: c
Explanation: Work done by the C pipe in 1 minute
$$\eqalign{ & = \frac{1}{{15}} – \left( {\frac{1}{{20}} + \frac{1}{{24}}} \right) \cr & = \left( {\frac{1}{{15}} – \frac{{11}}{{120}}} \right) \cr & = – \frac{1}{{40}}\,\left[ { – {\text{ve}}\,{\text{means}}\,{\text{emptying}}} \right] \cr} $$
Volume of $$\frac{1}{{40}}$$ part = 3 gallons.
Volume of whole = (3 × 40) gallons = 120 gallons

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