From a tank, completely filled to its brim, water equal to $\frac{2}{5}$ of its capacity was taken out. 130 litres of water was added to the tank leaving it only $\frac{1}{6}$ empty. Find the capacity of the tank.

Given:

From a tank, completely filled to its brim, water equal to $\frac{2}{5}$  of its capacity was taken out.

130 litres of water was added to the tank leaving it only $\frac{1}{6}$ empty.

To do: Here we have to find the capacity of the tank.

Solution:

Let capacity of the tank be = $x$ litres

If  $\frac{2x}{5}$ water is taken out remaining water in tank = $1\ -\ \frac{2 x}{5}\ =\ \frac{3x}{5}$

To this $\frac{3x}{5}$ water, 130 litres of water is added.

$\frac{3x}{5}\ +\ 130$

Now tank is  $\frac{1}{6}$ empty means it is $1\ -\ \frac{1}{6}\ =\ \frac{5x}{6}$ full

$\frac{3x}{5}\ +\ 130\ =\ \frac{5x}{6}$

$\frac{5x}{6}\ -\ \frac{3x}{5}\ =\ 130$

$\frac{25x}{30}\ -\ \frac{18x}{30}\ =\ 130$

$\frac{7x}{30}\ =\ 130$

$x\ =\ \frac{3900}{7}$

$x\ =$ 557.14 litres

So, capacity of the tank is 557.14 litres.

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Updated on: 10-Oct-2022

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