A container holds a mixture of grape juice and water. The ratio of grape juice to water is initially 5:2. If 15 litres of pure grape juice is added to the mixture, the new ratio of grape juice to water becomes 8:3. What was the initial total volume of the mixture (in litres)?
Show answer & explanation
Correct answer: D
Explanation
Given:
Initial Ratio (Juice : Water) = 5 : 2
15 liters of pure juice were added
New Ratio = 8 : 3
According to the formula:
Quantity = Ratio × x
Let the initial quantity be 7x
Juice = 5x
Water = 2x
New Juice quantity = 5x + 15
Water quantity = 2x
New Ratio:
(5x + 15) / 2x = 8/3
3(5x + 15) = 8(2x)
15x + 45 = 16x
x = 45
Total Initial Quantity = 7x = 7 × 45 = 315 liters