Multiple choice

Harsha is $40$ years old and Ritu is $60$ years old. How many years ago was the ratio of their ages $3\,\colon\,5$?

  1. $\;10$ years
  2. $\;20$ years
  3. $\;37$ years
  4. $\;5$ years
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A Correct answer
Explanation

Let x be the number of years ago. (40-x) / (60-x) = 3/5. 5(40-x) = 3(60-x). 200 - 5x = 180 - 3x. 20 = 2x, so x = 10.

AI explanation

Let the number of years ago be x, giving the equation (40 - x) / (60 - x) = 3 / 5. Cross-multiplying results in 200 - 5x = 180 - 3x, which means 20 = 2x and x = 10. The ratio of their ages was 3:5 exactly 10 years ago.

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