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    Question

    Ratio of present age of 'A' to that of 'B' is 4:7. If

    the age of 'B' three years hence from now will be 31 years, then after how many years, the ratio of the age of 'B' to that of 'A' will become 5:4?
    A 26 Correct Answer Incorrect Answer
    B 28 Correct Answer Incorrect Answer
    C 30 Correct Answer Incorrect Answer
    D 32 Correct Answer Incorrect Answer

    Solution

    Let the present ages of 'A' and 'B' be '4m' and '7m' years respectively.

    So, 7m + 3 = 31

    Or, 7m = 28

    So, 'm' = 4

    Present age of 'A' = 4m = 16 years
    Present age of 'B' = 7m = 28 years

    Let ratio of the ages of 'B' to 'A' becomes 5:4 after 'n' years.

    So, (16 + n) : (28 + n) = 4 : 5

    Or, 5 × (16 + n) = 4 × (28 + n)

    Or, 80 + 5n = 112 + 4n

    So, 'n' = 32

    Hence, option D.

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