The present ages of Rajib and his elder brother are in the ratio 5 : 7. After five year the ratio of their ages will be 3 : 4. Find Rajib's present age.

Question: The present ages of Rajib and his elder brother are in the ratio 5 : 7. After five year the ratio of their ages will be 3 : 4. Find Rajib's present age.

Solution:
Ratio of present ages of Rajib and his elder brother = 5 : 7
Let the present ages of Rajib and his elder brother be 5x and 7x.

After five years,
Age of Rajib = 5x + 5
and Age of elder Brother = 7x + 5
According to question, then the ratio of their ages = 3 : 4
⇒ (5x + 5) : (7x + 5) = 3 : 4
⇒ (5x + 5)/(7x + 5) = 3/4
⇒ 20x + 20 = 21x + 15
∴ x = 5

Thus, Present age of Rajib = 5x = 5 × 5 = 25 years