Question

If an acid and water are mixed in the ratio 5:6 to make a liquid and 20 more litres of acid is added, the ratio changes to 5:2 then what is the final volume of liquid?

• A. 10 litres
• B. 12 litres
• C. 20 litres
• D. 42 litres

Answer 1

The correct option is D

42 litres

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 turns to 5:2

Now let the volume of acid be $5y$ litres and volume of water in the liquid will 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 liquid
= $5y+2y$
= $7y$
= $7\times 3x$ $(\because y=3x)$
= 7 $\times$ 3 $\times$ 2 $(\because x=2)$
= 42 litres