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27 October, 06:16

4. The sum of the ages of a woman and her daughter is 46 years. In

4 years', time, the ratio of their ages will be 7:2. Find their

present age.

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Answers (1)
  1. 27 October, 06:33
    0
    Present age of woman = 38 years.

    Present age of Daughter = 8 years.

    Explanation:

    Given:

    The sum of the ages of a woman and her daughter = 46 years.

    In 4 years time, the ratio of their ages = 7:2.

    Solution:

    Let assume,

    Present age of woman = x years

    Present age of Daughter = y years

    as given,

    The sum of the ages of a woman and her daughter = 46 years.

    x+y = 46

    x = 46 - y ... (equation 1)

    and,

    In 4 years time, the ratio of their ages = 7:2.

    After 4 years,

    Age of woman = (x+4) years

    Age of daughter = (y+4) years

    → (x+4) : (y + 4) = 7:2

    → x+4/y+4 = 7/2

    → 46-y+4/y+4 = 7/2

    → 50-y/y+4 = 7/2

    →7y + 28 = 100-2y

    → 7y + 2y = 100 - 28

    → 9y = 72

    → y = 8

    so, y = Present age of Daughter = 8 years.

    Put the value of y = 8 in equation (1).

    → x = 46 - y

    → x = 46 - 8

    → x = 38

    Thus, the Present age of woman = x = 38 years.
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