Question
In an 84-liter mixture of petrol and oil, the ratio of
petrol to oil is 9:5. A certain amount of this mixture is removed and replaced with an equal amount of oil. If the final mixture has a ratio of petrol to oil as 3:4, determine the amount of the mixture that was withdrawn initially.Solution
ATQ, Initial quantity of petrol in the mixture = 84 × (9/14) = 54 liters Initial quantity of oil in the mixture = 84 × (5/14) = 30 liters Let the quantity of mixture that has been taken out be ‘14m’ liters So, quantity of petrol that has been taken out = 14m × (9/14) = ‘9m’ liters Quantity of oil that has been taken out = 14m × (5/14) = ‘5m’ liters According to question: {(54 – 9m)/(30 – 5m + 14m)} = (3/4) Or, 4 × (54 – 9m) = 3 × (30 + 9m) Or, 72 – 12m = 30 + 9m Or, 21m = 42 Or, m = 2 Quantity of mixture that has been taken out = 14 × 2 = 28 liters
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