Question : Two pipes A and B can fill a tank in 12 minutes and 24 minutes, respectively, while a third pipe C can empty the full tank in 32 minutes. All three pipes are opened simultaneously. However, pipe C is closed 2 minutes before the tank is filled. In how much time (in minutes) will the tank be full?
Option 1: 9
Option 2: 10
Option 3: 12
Option 4: 8
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Correct Answer: 10
Solution :
LCM of 12, 24 and 32 is 96
The capacity of the tank = 96 unit
Efficiency of pipe A = $\frac{96}{12}$
= 8 unit/min
Efficiency of pipe B = $\frac{96}{24}$
= 4 unit/min
Efficiency of pipe C = $\frac{96}{32}$
= – 3 unit/min
Combined efficiency of A + B + C = 9 unit/min
Let if C is not closed 2 minutes before then
Work done by C in 2 minutes = 2 × – 3 = – 6 unit
Total work done by all pipes = 96 + (– 6) = 90 unit
Required time = $\frac{\text{total work}}{\text{total efficiency }}$
Required time = $\frac{90}{9}$
= 10 minutes
Hence, the correct answer is 10.
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