Multiple choice

Ten (10) years before, the ages of a mother and her daughter were in the ratio 3 : 1. In another 10 years from now, the ratio of their ages will be 13 : 7. What are their present ages?

  1. 39 years, 21 years

  2. 55 years, 25 years

  3. 75 years, 25 years

  4. 49 years, 31 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M and D be current ages. (M-10)/(D-10) = 3/1 => M-10 = 3D-30 => M = 3D-20. (M+10)/(D+10) = 13/7 => 7M+70 = 13D+130 => 7M-13D = 60. Substitute M: 7(3D-20) - 13D = 60 => 21D - 140 - 13D = 60 => 8D = 200 => D = 25. M = 3(25)-20 = 55.

AI explanation

Let the present age of the mother be x and the daughter be y; from the first condition 10 years ago, (x - 10) / (y - 10) = 3 / 1, so x = 3y - 20. The second condition states that (x + 10) / (y + 10) = 13 / 7, which gives 7x + 70 = 13y + 130. Substituting the first equation into the second yields 21y - 140 + 70 = 13y + 130, which simplifies to 8y = 200 and y = 25. Thus, the mother's present age is 3(25) - 20 = 55 years, making their present ages 55 years and 25 years.

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