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Discussion :: Ratio and Proportion

  1. Vessels A and B contain mixtures of milk and water in the ratios 4: 5and 5: 1respectively. In what ratio should quantities of the mixture be taken from A and B to form a mixture in which milk to water is in the ratio 5: 4?

  2. A.
    2: 5
    B.
    4: 3
    C.
    5: 2
    D.
    2: 3

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    Answer : Option C

    Explanation :

    Let the quantity of vessels A and B in the ratio x: y to form a mixture of water and milk in the ratio 4: 5.
    Or, Milk: water = 5: 4.
    From vessel A, milk: water = 4x/9: 5x/9
    From vessel B, milk: water = 5y/6: 1y/6

    Now, ATQ quantities of the mixture should be taken from A and B.
    Ratio of milk: water = [4x/9 +5y/6]: [5x/9+ 1y/6] = 5/4
    Take the LCM of 9 and 6 = 54
    Or, [24x + 45y]/54: [30x+9y]/54 = 5/4
    Or, [8x + 15 y]: [10x + 3y] = 5/4
    Or, [8x + 15y] * 4 = [10x + 3y] * 5
    Or, (60-15) y = (50-32) x
    Or, 45y = 18x
    Or, 5y = 2x
    Or, x: y = 5: 2
    Hence, the quantity of mixture should be taken from A and B in the ratio 5: 2.


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