Question : Two pipes can fill a tank alone in 20 hours and 24 hours respectively and an outlet pipe alone can empty 20 gallons of water per hour. All three pipes working together can fill the same empty tank in 40 hours. What is the capacity of the tank?
Option 1: 450 gallons
Option 2: 300 gallons
Option 3: 600 gallons
Option 4: 480 gallons
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Correct Answer: 300 gallons
Solution : Let the total work = capacity of the tank ($C$). According to the question Rate of doing work for first pipe = $\frac{C}{20}$ And rate of doing work for second pipe = $\frac{C}{24}$ The rate of emptying by the outlet pipe is 20 gallons per hour When all three pipes are working together, they can fill the tank in 40 hours ⇒ $\frac{C}{20}$ + $\frac{C}{24}$ − 20 = $\frac{C}{40}$ ⇒ $6C + 5C − 2400 = 3C$ ⇒ $8C = 2400$ ⇒ $C = \frac{2400}{8}$ = 300 gallons Hence, the correct answer is 300 gallons.
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