Fathers age is three times the sum of ages of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.

Explanation

Let the present age of the man be x years and the sum of the present ages of his two sons by y years. Then,
` x = 3y rArr x- 3y = 0 " " `… (i)
Man's age after 5 years = ( x + 5) years.
Sum of the ages of his two sons after 5 years = `( y + 5 + 5)` years
` = ( y + 10)` years.
` therefore (x + 5) = 2(y+ 10 ) rArr x - 2y = 15" " `... (ii)
On subtracting (i) from (ii), we get y = 15.
Putting ` y = 15 ` in (i), we get ` x = 45`
` therefore x = 45 and y = 15 `
Hence, the present age of the man is 45 years.