A tank (of capacity 160 L) has one inlet, A and one outlet, B. Inlet A, alone can fill the empty tank in 6 h and outlet B alone can empty the full tank in 24 h. In how many hours will inlet A fill 16 L water in the tank when outlet B is also open?

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\frac{4}{5}

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\frac{11}{5}

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\frac{1}{2}

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\frac{1}{5}

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Solution

The correct option is B $\frac{4}{5}$
Capacity of the tank =160L
Let, the inlet (pipe) A fill the full tank in 'x' h=6h
and the outlet (pipe) B empty the full tank in y h=24h
Then, time taken to fill the full tank= $\frac{x y}{y - x} \frac{6 \times 24}{24 - 6} = \frac{6 \times 24}{18} = 8 h$
160 L(Full tank) of water fill in the tank in 8h.
Then, $160 L \to 8 h 16 L \to \frac{8}{10} h = \frac{4}{5} h$

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\frac{1}{2}

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