A tank is full. Pipes A and B can drain the tank in 10 hours and 15 hours, respectively, while pipe C can fill the tank in 12 hours. Pipes A and B run for 2 hours, after which pipe C is also turned on. How many hours will it take to empty the tank completely?
10 hours
Let the tank capacity be 60 units (LCM of 10, 15 and 12). Pipe A drains 6 units/hr, pipe B drains 4 units/hr, pipe C fills 5 units/hr.
In the first 2 hours, only A and B run, draining \(2\times(6+4) = 20\) units, leaving \(60-20=40\) units.
After 2 hours, with C also running, the net drain rate becomes \(6+4-5 = 5\) units/hr.
Time to drain the remaining 40 units: \(\dfrac{40}{5} = 8\) hours.
Total time: \(2+8 = 10\) hours.
Hence, it takes 10 hours to empty the tank completely.
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