Multiple choice

11 years ago, the ratio of the ages of Eliana and her daughter was 30 : 1. The present age of Eliana's Son is 4 years more than the present age of Eliana's daughter. 10 years ago, the age of Eliana's husband was 5/2th of the present age of Eliana's daughter. If the average of the present age of all four persons is 27.25 years, then find the age of Eliana's husband after 11 years.

  1. 51 years

  2. 53 years

  3. 49 years

  4. 62 years

  5. None of these
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A Correct answer
Explanation

Let E and D be present ages. 11 years ago: (E-11)/(D-11) = 30/1. E-11 = 30D - 330 => E = 30D - 319. Average of 4 people (E, D, S, H) = 27.25 => E+D+S+H = 109. S = D+4. H-10 = 2.5D => H = 2.5D + 10. Substitute: (30D-319) + D + (D+4) + (2.5D+10) = 109. 34.5D - 305 = 109 => 34.5D = 414 => D = 12. E = 30(12)-319 = 41. H = 2.5(12)+10 = 40. Age of husband after 11 years = 40 + 11 = 51.

AI explanation

Let the present age of Eliana be E and her daughter be D; from the ratio 11 years ago, E - 11 = 30(D - 11). The son's age is D + 4, and the husband's age is 2.5D + 10. The average of all four ages is 27.25, so E + D + (D + 4) + (2.5D + 10) = 109, which simplifies to E + 4.5D = 95; substituting E = 30D - 319 gives 34.5D = 414, so D = 12. The husband's present age is 2.5(12) + 10 = 40, and his age after 11 years is 51 years.

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