Question

Pipes A, B, and C alone can fill a tank in 25 minutes, 75 minutes, and 50 minutes, respectively while a tap alone can empty the tank in 150 minutes. If pipe A and the tap opened together and after 15 minutes pipe A is closed and B and C together is opened, then in how many minutes will the tank filled completely?

• A. 23.15 minutes
• B. 31.25 minutes
• C. 42.75 minutes
• D. 33.75 minutes

Answer 1

The Correct Option is D

The correct option is (D): 33.75 minutes.
Pipe A alone can fill the tank in 25 minutes
Pipe B alone can fill the tank in 75 minutes
Pipe C alone can fill the tank in 50 minutes
The tap alone can empty the tank in 150 minutes.
Let the tank be filled in T minutes.
15(\(\frac{1}{25} \)- \(\frac{1}{150} \)) + (T - 15)(\(\frac{1}{75} \) + \(\frac{1}{50} \) - \(\frac{1}{150} \)) = 1
=> \(\frac{1}{2} \) + (T - 15) * \(\frac{2}{75} \)= 1
=> T - 15 = \(\frac{1}{2} \) * \(\frac{75}{2} \) = 18.75
=> T = 33.75 minutes.