Question
The ratio of the husband’s age three years from now to
the wife’s age two years ago is 9:7. Additionally, the ratio of the husband’s age one year ago to the wife’s age ten years from now is 4:5. Determine the current age of the wife.Solution
Let the present ages of the husband and that of the wife be 'x' years and 'y' years, respectively According to the question, (x + 3):(y - 2) = 9:7 Or, 7x + 21 = 9y - 18 Or, 7x = 9y - 39 - [I] Also, (x - 1):(y + 10) = 4:5 Or, 5x - 5 = 4y + 40 Or, 5x = 4y + 45 - [II] Multiplying [II] by 1.4 7x = 5.6y + 63 So, 5.6y + 63 = 9y - 39 Or, 3.4y = 102 So, y = 102 ÷ 3.4 = 30
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