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:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4.4
In 36 litres of the mixture, the juice and water are shared in the ratio 10 : x:
\( \displaystyle \text{juice} = \frac{360}{10 + x},\quad \text{water} = \frac{36x}{10 + x} \)
Adding 9 litres of water changes only the water. The new ratio is 5 : 4:
\( \displaystyle 4 \times \frac{360}{10 + x} = 5\left(\frac{36x}{10 + x} + 9\right) \)
Multiplying by 10 + x:
\(1440 = 180x + 45(10 + x)\)
\(1440 = 450 + 225x\)
\(225x = 990\)
\(x = 4.4\)
Check: juice = 360/14.4 = 25 litres, water = 11 + 9 = 20 litres, and 25 : 20 = 5 : 4.