Question 63

A jar contains a blend of a fruit juice and water in the ratio 5 : x. When 1 litre of water is added to 4 litres of the blend the ratio of fruit juice to water becomes 1 : 1. What is the value of x?

Solution

In 4 ltr :

Fruit juice =$$4\times\frac{5}{5+x}=\frac{20}{5+x}\ .$$

And, Water = $$4\times\frac{x}{5+x}=\frac{4x}{5+x}\ .$$

According to question ,

$$\frac{\frac{20}{5+x}}{\frac4{x}{5+x}+1}=\frac{1}{1}\ .$$

or, $$\frac{20}{5+x}=\frac{4x}{5+x}+1\ .$$

or, $$20-x=5+4x\ .$$

or, $$x=\frac{15}{5}=3\ .$$

So, A is correct choice.

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