The sum of the present ages of a father and his son is 78 years. After five years, the ratio of their ages becomes 7 : 4. What is the present age (in years) of the father?

51

The ratio of ages of a father and son five years ahead is 7 : 4 

To calculate their present ages, we subtract 5 from each

Father's present age = (7r - 5) years 

Son's present ages = (4r - 5) years  

Given, Sum of present ages = 78 years 

⇒ (7r - 5) + (4r - 5) = 78 

⇒            11r - 10    = 78

⇒                  11r     = 88    or r = 8

Present ages of father = 7x8 - 5  = 51 years