Question
A container has a mixture of juice and soda in the ratio
4:1. If half of the mixture is removed and replaced by 15 litres of soda, the resulting ratio of juice to soda becomes 8:7. What was the original quantity of the mixture?Solution
ATQ,
Let the initial quantity of the mixture = ‘2x’ litres Then, quantity of the mixture left after removing half = ‘x’ litres In ‘x’ litres of mixture, let quantity of juice = ‘4y’ litres In ‘x’ litres of mixture, let quantity of soda = ‘1y’ litres According to the question, 4y / (y + 15) = 8/7 ⇒ 7 × 4y = 8 × (y + 15) ⇒ 28y = 8y + 120 ⇒ 20y = 120 ⇒ y = 6 So, x = 4y + y = 5y = 5 × 6 = 30 litres Initial quantity of the mixture = 2x = 2 × 30 = 60 litres
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