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

Solution(By Examveda Team)

Let the age of the son and the daughter of Poorvi be 6a years and 7a years respectively.
5 years hence, present age of son = 6a - 5 and present age of daughter = 7a - 5
According to the question,
Eight years ago, the age of Poorvi = 6a - 5 + 7a - 5 = 13a - 10
So, present age of Poorvi = 13a - 10 + 8 = 13a - 2
Since, present age of Poorvi husband = 3 (6a - 5)
The difference of present age of Poorvi husband and Poorvi = 7 (Given)
$$\eqalign{ & {\text{3}}\left( {6a - 5} \right) - \left( {13a - 2} \right) = 7 \cr & \Rightarrow 18a - 15 - 13a + 2 = 7 \cr & \Rightarrow 5a = 20 \cr & \Rightarrow a = 4 \cr} $$
The present age of daughter
= (7a - 5)
= 7 × 4 - 5
= 23 years