A vessel holds 64 litres of pure oil. A certain amount is taken out and replaced with a cheaper oil, and this is done twice. 49 litres of the pure oil are left. How much was taken out each time?

Explanation

1. 01

   If $x$ litres go each time, $64\left(1 - \frac{x}{64}\right)^{2} = 49$, so $\left(1 - \frac{x}{64}\right)^{2} = \frac{49}{64}$.

2. 02

   $1 - \frac{x}{64} = \frac{7}{8}$, so $x = 8$ litres.