Solve the following mathematical problems with sufficient calculations.

A pipe can fill up an empty tank in 12 minutes. Another pipe flows out 14 liter of water per minute. If the two pipes are opened together and the empty tank is filled up in 96 minutes, how much water does the tank contain?
(Pipe & Cistern)

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

In 1 minute, first pipe can fill $\frac{1}{12}$ part of tank.

Let, second pipe can empty the tank in x minutes.

∴ In 1 minute, it can empty $\frac{1}{x}$ part of tank.

That means, the tank is filled in 1 minutes $(\frac{1}{12} - \frac{1}{x})$ Part

According to question, $\frac{1}{12} - \frac{1}{x} = \frac{1}{96}$

$\Rightarrow \frac{1}{x} = \frac{1}{12} - \frac{1}{96} = \frac{8 - 1}{96} = \frac{7}{96}$

$∴ x = \frac{96}{7} m i n u t e s$

∴ The tank contains $= 14 \times \frac{96}{7}$ = 192 liters.

1 year ago

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