Multiple choice

The ratio of the present ages of Anuradha and her mother is 1 : 2, respectively. The ratio of their ages 6 years hence would be 11 : 20. What was the ratio of their ages 9 years ago?

  1. 3 : 5

  2. 2 : 7

  3. 1 : 4

  4. 2 : 5

  5. None of these
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D Correct answer
AI explanation

Let the present ages of Anuradha and her mother be x and 2x years. Six years hence, their ages will be x + 6 and 2x + 6, giving the ratio equation 20(x + 6) = 11(2x + 6). Solving 20x + 120 = 22x + 66 results in 2x = 54, so x = 27; thus, their present ages are 27 and 54. Nine years ago, their ages were 27 - 9 = 18 and 54 - 9 = 45, making the ratio 18:45, which simplifies to 2:5.

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