Question
A vessel holds ‘4x’ litres of milk and ‘3y’
litres of water. When 25 litres of water is poured into it, the milk to water ratio becomes 8:7. However, if 15 litres of water is added instead, the ratio of water to milk becomes 5:6. What is the original quantity of milk (in litres) in the vessel?Solution
ATQ,
According to the question, {4x/(3y + 25)} = 8/7 Or, 28x = 24y + 200 Or, 7x – 6y = 50…….. (1) Also, {4x/(3y + 15)} = 6/5 Or, 20x = 18y + 90 Or, 10x – 9y = 45…….. (2) Equation (1) × 3 – Equation (2) × 2, we get 21x – 18y – 20x + 18y = 150 – 90 Or, x = 60 So, initial quantity of milk in the mixture = 4x = 4 × 60 = 240 litres
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