Multiple choice

Eight years ago, Poorvi's age was equal to the sum of the present ages of her one son and one daughter. Five years hence, the ratio of the ages of her daughter and her son that time will be 7 : 6, respectively. If Poorvi's husband is 7 years elder to her and his present age is three times the present age of their son, then what is the present age of the daughter?

  1. 15 years

  2. 23 years

  3. 19 years

  4. 27 years

  5. 13 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P, S, and D be the present ages of Poorvi, son, and daughter. From the first condition, P-8 = S+D. From the second, (D+5)/(S+5) = 7/6, so 6D+30 = 7S+35, or 6D-7S = 5. Given the husband is P+7 and P+7 = 3S, we have P = 3S-7. Substituting P into the first equation: (3S-7)-8 = S+D, so 2S-D = 15. Solving the system 6D-7S = 5 and 2S-D = 15 yields D = 23.

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