Question

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:

• A. 4
• B. 4.4
• C. 5
• D. 8

Answer 1

The Correct Option is B

Let the amount of apple juice in the mixture be 10 parts and water be \(x\) parts. The total quantity of the mixture is \(10 + x\) parts.

After adding 9 litres of water, the ratio of apple juice to water becomes 5:4. This gives:
\(\frac{36 \cdot \frac{10}{10+x}}{36 \cdot \frac{x}{10+x} + 9} = \frac{5}{4}.\)

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

Clear the fraction and simplify:
\(1440 = 180x + 45(10 + x),\)
\(1440 = 180x + 450 + 45x \quad \Rightarrow \quad 1440 - 450 = 225x.\)
\(990 = 225x \quad \Rightarrow \quad x = \frac{990}{225} = 4.4.\)

Thus, \(x = 4.4\)