Multiple choice

18 months ago, Dev's age was 2.5 times Rex's age. After 4 months from now, Dev's age will be double of Rex's age. Find the sum of their present ages?

  1. 15 years 10 months

  2. 15 years 8 months

  3. 19 years

  4. 16 years 2 months
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A Correct answer
Explanation

Let present ages be D and R. 18 months ago: D - 1.5 = 2.5(R - 1.5), so D = 2.5R - 2.25. After 4 months from now: D + 1/3 = 2(R + 1/3), so D = 2R + 1/3. Equating: 2.5R - 2.25 = 2R + 1/3, giving 0.5R = 2.583, so R = 5.167 years = 5 years 2 months. D = 2(5.167) + 1/3 = 10.667 years = 10 years 8 months. Sum = 15 years 10 months.

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