Question

    How many litres of liquid A was contained by the Can

    initially? Quantity I: A Can contains a mixture of two liquids A and B in the ratio 7: 5. When 9 litres of mixture are drawn off and the Can is filled with B, the ratio of A and B becomes 7: 9 . Quantity II: A Can contains a mixture of two liquids A and B in the ratio 4:1. When 10 litres of mixture are drawn off and the Can is filled with B, the ratio of A and B becomes 2: 3 . In each of the following questions, read the given statements and compare the two given quantities on it basis.  Give answer:
    A Quantity I > Quantity II Correct Answer Incorrect Answer
    B Quantity I < Quantity II Correct Answer Incorrect Answer
    C Quantity I ≥ Quantity II Correct Answer Incorrect Answer
    D Quantity I ≤ Quantity II Correct Answer Incorrect Answer
    E Quantity I = Quantity II or No relation can be established Correct Answer Incorrect Answer

    Solution

    Quantity I. Suppose the Can initially contains 7x and 5x litres of mixtures A and B respectively.   Quantity of A in mixture left = 7x – 7/12 of 9  = 7x – (21/4) Litres   Quantity of B in mixture left =5x – 5/12 of 9 = 5x –  (15/4) Litres     {7x – (21/4)} / {5x – (15/4) + 9 } = 7/9   (28x-21)/(20x+21) = 7/9   So 252x – 189 = 140x + 147 or x = 3.   Or Quantity of A in the Can initially = 7x = 21   Quantity II. Suppose the Can initially contains x and 4x litres of mixtures A and B respectively.   Quantity of A in mixture left = (4x-4/5 of 10) =(4x-8) litres   Quantity of B in mixture left = (1x-1/5 of 10) = (x-2) liters   (4x-8)/(x-2+10) = 2/3   Or 12x – 24 = 2x + 16    So x= 4.   Or Quantity of A in the Can initially = 4x = 16   Hence, Quantity I > Quantity II

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