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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.