Question 124

A water tank has one inlet, A and one outlet, B. A takes 5 hours to fill the empty tank, when B is not open and B takes 8 hours to empty the full tank. If the tank is three fifth full, how much time will it take to fill the tank completely when both A and B are opened simultaneously ? (in hours)

Solution

Part of tank filled by A and B in 1 hour

= $$\frac{1}{5} - \frac{1}{8} = \frac{3}{40}$$

=> Time taken to fill the tank completely = $$\frac{40}{3}$$ hrs

$$\therefore$$ Time taken to fill two-fifth part of tank

= $$\frac{2}{5} \times \frac{40}{3}$$

= $$\frac{16}{3} = 5\frac{1}{3}$$ hrs

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