A mixture contains apple juice and water in the ratio 10 : x. When 36 litres of the mixture and 9 litres of water are mixed, the ratio of apple juice and water becomes 5 : 4. The value of x is:

4.4

The correct answer is Option (2) → 4.4

$\text{Initial ratio of apple juice : water } = 10:x.$

$\text{From 36 litres mixture, apple juice} = \frac{10}{10+x}\cdot36,\;\text{water}=\frac{x}{10+x}\cdot36.$

$\text{After adding 9 litres water,}$

$\text{Apple juice}=\frac{360}{10+x},\;\text{Water}=\frac{36x}{10+x}+9.$

$\text{Final ratio }=\frac{\frac{360}{10+x}}{\frac{36x}{10+x}+9}=\frac{5}{4}.$

$4\cdot\frac{360}{10+x}=5\left(\frac{36x}{10+x}+9\right).$

$\frac{1440}{10+x}=\frac{180x}{10+x}+45.$

$1440=180x+45(10+x).$

$1440=180x+450+45x.$

$225x=990.$

$x=\frac{990}{225}=\frac{22}{5}.$