Question : Pipes P and Q can fill a tank in 18 and 27 minutes, respectively, whereas pipe R can empty the full tank in 54 minutes. P and Q were opened together for 6 minutes and then closed and R was opened. The tank was emptied by R alone in:
Option 1: 35 minutes
Option 2: 45 minutes
Option 3: 30 minutes
Option 4: 40 minutes
Correct Answer: 30 minutes
Solution :
Given:
Pipe P filling time = 18 minutes
Pipe Q filling time = 27 minutes
Pipe R empty time = 54 minutes
P and Q opened for 6 minutes.
Now,
Capacity of tank = LCM of 18, 27, and 54 = 54 units
Efficiency of P = $\frac{54}{18}$ = 3
Efficiency of Q = $\frac{54}{27}$ = 2
Efficiency of R = $\frac{54}{54}$ = 1
Work done by P and Q in 6 min = $(3 + 2)\times 6 = 30$
Pipe R empty the tank = $\frac{30}{1} = 30$ min
Hence the correct answer is 30 minutes.
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