Question
A container has ‘2x’ litres of juice and ‘3y’ litres of soda. If 24 litres of soda is added to the container, the ratio of juice to soda becomes 5:6. However, if only 12 litres of soda is added, the ratio of soda to juice becomes 3:5. What is the original quantity of juice in the container?
Solution
ATQ,
{2x / (3y + 24)} = 5/6 ⇒ 12x = 15y + 120 ⇒ 4x – 5y = 40 ……(1) Also, {(3y + 12) / 2x} = 3/5 ⇒ 5(3y + 12) = 6x ⇒ 15y + 60 = 6x ⇒ 6x – 15y = 60 ……(2) Now, (1) × 3: 12x – 15y = 120 (2): 6x – 15y = 60 Subtracting: 6x = 60 x = 10 ∴ Initial juice = 2x = 2 × 10 = 20 litres
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