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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 the 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?

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 the 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? Correct Answer 10

Shortcut Trick

Calculation:

Let the capacity of tank be 96 unit   

Efficiency of pipe A = 96 ÷ 12 = 8 unit/min

Efficiency of pipe B = 96 ÷ 24 = 4 unit/min

Efficiency of pipe C = 96 ÷ 32 = -3 unit/min

Combined efficiency of A + B + C = 9 unit/min 

Let if C is not closed 2 min before then 

Work done by C in 2 min = 2 × -3 = -6 unit 

So, Total work done by all pipes = 96 + (-6) = 90 unit 

So, Required time = total work/total efficiency 

So, Required time = 90 ÷ 9 = 10 min

∴ The required time is 10 min.

Efficiency of pipe A = 96 ÷ 12 = 8 unit/min

Efficiency of pipe B = 96 ÷ 24 = 4 unit/min

Efficiency of pipe C = 96 ÷ 32 = -3 unit/min

Combined efficiency of A + B + C = 9 unit/min 

Combined efficiency of A + B = 12 unit/min

According to the question 

Pipe C is closed 2 min before the tank is filled 

So, In last 2 min work done by A + B = 12 × 2 = 24 unit

Rest capacity of tank = 96 - 24 = 72 unit 

Now Rest capacity of tank is filled by all the pipes 

So, Time = 72 ÷ 9 = 8 min 

∴ Total time to fill the tank = 2 min + 8 min 10 min.

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