Question
Eight years ago, the sum of the ages of Helen and Karen
was 50 years. Eight years hence, the ratio of their ages will be 9:11. Find the current age of Helen.Solution
ATQ, Let the ages of Helen and Karen in eight years be 9x and 11x respectively. Their combined age eight years hence = 9x+11x=20x. Eight years ago, their combined ages were 50. Thus, their combined ages today = 50+16=66. 20x=66+16=82. Solving for x, 20x = 82 = x = 82/20 = 4.1 Age of Helen eight years hence = 9x = 9×4.1 = 36.9 years. Current age of Helen = 36.9 − 8 = 28.9 years.
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