Question

If an acid and water are mixed in the ratio 5:6 to make a liquid. When 20 more litres of acid is added, the ratio changes to 5:2, then how many litres of acid does the liquid contain now?

Answer 1

Initially given the ratio of acid to water = 5:6

$\therefore$ Let the volume of acid be 5$x$ litres and volume of water be 6$x$ litres.

Now 20 more litres of acid is added and the ratio becomes 5:2

Hence the new volume of acid will be $5y$ litres and volume of water be $2y$ litres.

$\Rightarrow$ $5x+20=5y$ --------(1)

and $6x=2y$

$\Rightarrow$ $y=3x$ -------(2)

Now put the value of $y$ in (1)

$\Rightarrow$ $5x+20=5\left(3x\right)$

$\Rightarrow$ $5x+20=15x$

$\Rightarrow$ $10x=20$

$\Rightarrow$ $x=2$

$\therefore$ The volume of acid that liquid contains
= $5y$
= $15x$ [from (2)]
= 15 $\times$ 2 = 30 litres