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Pipe A which can fill a tank in 20 minutes is kept open for 5 minutes when the tank is empty. Then Pipe B which can fill the tank in 30 minutes is also opened. How long after Pipe A is opened will the tank be full?
A) 12 minutes
B) 17 minutes
C) 16 minutes
D) 14 minutes
Correct answer:
D) 14 minutes
Description for Correct answer:
Pipe A fills \( \Large \frac{1}{20} \)th of the tank every minute. ln 5 minutes, it will fill \( \Large 5 \times \frac{1}{20} = \frac{1}{4} \)th of the tank.
After 5 minutes, Pipe B is also opened.
Together, Pipe A and Pipe B fill \( \Large \frac{1}{20}+\frac{1}{30}=\frac{3+2}{60}=\frac{1}{12} \)th of the tank every minute.
Together the pipes will fill an empty tank in 12 minutes.
As Pipe A alone had filled 1/4th of the tank by the time Pipe B was opened, only 3/4ths of the tank needs to be filled when the 2 pipes are working together.
To fill 3/4ths the tank, the two pipes will take \( \Large \frac{3}{4} \times 12 = 9\ min. \)
And, the total time taken = 5 + 9 = 14 minutes.
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