Question

A year hence a father will be 5 times as old as his son. Two years ago the father was three times as old as his son will be in 4 years hence from now. Find their present age.​

Answer 1

Step-by-step explanation:

let father's present age = x

let son's present age = y

father's age after one year = x + 1

son's age after one year = y + 1

therefore x + 1 = 5 (y + 1)

=> x + 1 = 5y + 5

=> x - 5y = 4 -------------(1)

father's age two years ago = x - 2

son's age four years from now = y + 4

therefore x - 2 = 3 (y + 4)

=> x - 2 = 3y + 12

=> x - 3y = 14------------(2)

solve equations (1) and (2)

=> x - 5y = 4-------------(1)

x - 3y = 14------------(2)

equation (1) - (2)

- 2y = -10

=> y = 5 and x = 29

father's age => x = 29 years

son's age => y = 5 years