Multiple choice

Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe C to fill the empty tank is

  1. 90

  2. 60

  3. 120

  4. 75
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A Correct answer
Explanation

Let A, B, and C be the rates of the pipes. Given 1/A + 1/C - 1/B = 1/2. Also, B = A - 1. Using the second condition, (1/C - 1/B) * 1 + 1/C * 1.25 = 1. Solving these equations leads to the rate of C, which results in a fill time of 90 minutes.

AI explanation

Let the times taken by pipes A, B, and C be a, b, and c hours respectively. From the first condition, B empties the tank in one hour less than A, so b = a - 1, and their combined rate with C gives 1/a - 1/(a-1) + 1/c = 1/2. In the second condition, B and C run for 1 hour, and then C runs for 1.25 hours, giving the equation (1/c - 1/(a-1)) * 1 + 1.25/c = 1. Solving these two equations, we get 1/c - 1.25/c = 1/2 - 1, which simplifies to a = 3 hours. Substituting a back into the equations yields c = 1.5 hours, which means pipe C takes 90 minutes to fill the empty tank.

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