Pipes P and Q can fill the tank in 18 and 27 minutes respectively, while pipe R can empty the full tank in 54 minutes. After P and Q are opened together for 6 minutes, they are closed and R is opened. Find the time taken by R alone to empty the tank.
Show answer & explanation
Correct answer: A
Explanation
The correct Answer is option 1 i.e. 30 minutes.
Pipes P and Q can fill in 18 and 27 minutes, respectively, whereas pipe R can empty the filled tank in 54 minutes
Suppose the capacity of the tank = 54 units (LCM of 18, 27, and 54)
Efficiency = Work/Time
So,
Efficiency of P = 54/18 = 3
Efficiency of Q = 54/27 = 2
Efficiency of R = 54/54 = 1
P and Q were opened together for 6 minutes
So,
Quantity of water filled = (3 + 2) × 6 = 30 units
Now R empties the tank i.e. 30 units
So,
Time taken by R = 30/1 = 30 minutes