Question

# 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?

A
2.4
B
3.6
C
6
D
60

Solution

## The correct option is C $$3.6$$Work efficiency of pipe A in filling tank = $$\dfrac{1}{2}$$ per hour Work efficiency of pipe B in emptying tank = $$-\dfrac{1}{3}$$ per hour $$\therefore$$ work done by A and B together = $$\dfrac{1}{2} - \dfrac{1}{3} = \dfrac{1}{6}$$per hour Hence time taken to fill the tank  $$100$$% = $$6$$ hours $$\therefore$$ time taken to fill $$60$$% = $$\dfrac{6\times 60}{100}$$  = $$3.6$$hours Answer is option BMathematics

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