A and B pipes can fill a tank in 10 and 20 minutes, respectively. Pipe C can empty the tank in 30 minutes. All three pipes are opened at a time in the beginning. However, pipe C is closed 2 minutes before the tank is filled. At what time will the tank be full (in minutes)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 8.
Let the total time taken by the tank to fill the tank be n
A and B pipes can fill a tank in 10 and 20 minutes, respectively.
Pipe C can empty the tank in 30 minutes.
L.C.M(10, 20, and 30) = 60
The efficiency of Pipe A = 60/10 = 6 units
The efficiency of Pipe B = 60/20 = 3 units
The efficiency of Pipe C = 60/30 = 2 units
So,
⇒ (6 + 3 - 2) × (n - 2) + 9 × 2 = 60
⇒ 7(n - 2) + 18 = 60
⇒ 7n - 14 + 18 = 60
⇒ 7n + 4 = 60
⇒ 7n = 56
⇒ n = 8
So, The time taken by the tank is 8 minutes