Question
Currently, Shweta and Rajni's ages are in the ratio of
5:4. Five years from now, the ages of Priya and Rajni will have a ratio of 7:5. Gautam is 10 years older than Priya. The average current age of Shweta, Rajni, Priya, and Gautam is 28.75 years. Determine Gautam's age five years ago.Solution
ATQ, Let the present age of Shweta and Rajni be '5a' years and '4a' years respectively. Present age of Priya = [{(4a + 5) × (7/5)} – 5] years = (5.6a + 2) years Therefore, present age of Gautam = (5.6a + 2 + 10) = (5.6a + 12) years ATQ, 5a + 4a + 5.6a + 2 + 5.6a + 12 = 28.75 × 4 Or, a = 101/20.2 = 5 years Therefore, age of Gautam 5 years ago = 5.a + 12 – 5 = 35 years
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