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    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 If the final mixture has a ratio of petrol to oil as 3:4, determine the amount of the mixture that was withdrawn initially.
    A 25 liters Correct Answer Incorrect Answer
    B 20 liters Correct Answer Incorrect Answer
    C 35 liters Correct Answer Incorrect Answer
    D 28 liters Correct Answer Incorrect Answer
    E none of these Correct Answer Incorrect Answer

    Solution

    ATQ, Initial quantity of petrol in the mixture = 84 ร— (9/14) = 54 liters Initial quantity of oil in the mixture = 84 ร— (5/14) = 30 liters Let the quantity of mixture that has been taken out be โ€˜14mโ€™ liters So, quantity of petrol that has been taken out = 14m ร— (9/14) = โ€˜9mโ€™ liters Quantity of oil that has been taken out = 14m ร— (5/14) = โ€˜5mโ€™ liters According to question: {(54 โ€“ 9m)/(30 โ€“ 5m + 14m)} = (3/4) Or, 4 ร— (54 โ€“ 9m) = 3 ร— (30 + 9m) Or, 72 โ€“ 12m = 30 + 9m Or, 21m = 42 Or, m = 2 Quantity of mixture that has been taken out = 14 ร— 2 = 28 liters

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