Multiple choice

One year ago, Promila was four times as old as her daughter Sakshi. Six years hence, Promila's age will exceed her daughter's age by 9 years. The ratio of the present ages of Promila and her daughter is:

  1. 9:2

  2. 11 : 3

  3. 12:5

  4. 13 : 4
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D Correct answer
Explanation

Let P and S be present ages. One year ago: P-1 = 4(S-1). Six years hence: (P+6) - (S+6) = 9, which simplifies to P - S = 9. Solving the system: P = S + 9. Substituting into the first: S + 9 - 1 = 4S - 4, so 12 = 3S, S = 4. Then P = 13. The ratio is 13:4.

AI explanation

Six years hence, the difference between Promila's and Sakshi's ages will be 9 years, and because the age difference remains constant over time, their present age difference is also 9 years. One year ago, Promila was 4 times as old as Sakshi, meaning the difference between their ages at that time was 3 times Sakshi's age one year ago. Setting 3 times Sakshi's age equal to 9 years shows Sakshi was 3 years old one year ago, making her present age 4 years and Promila's present age 4 plus 9, which is 13 years. The ratio of their present ages is therefore 13 to 4.

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