A water tank has two pipes to fill it. Pipe A can fill the tank in $2$ hours , only if tank is empty. Pipe B can empty the tank in $3$ hours, only if tank is full. If both the pipes start at the same time when the task is empty, calculate the number of hours will it take for the tank to be filled to $60\%$ of its capacity?

Pipe A fills 1/2 of the tank per hour and pipe B empties 1/3 per hour, so the net rate is 1/2 - 1/3 = 1/6 of the tank per hour. To fill 60% of the tank, the required work is 0.6. The time taken is 0.6 / (1/6) = 3.6 hours.

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