Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

Let        present age of Jacob                     = x year

And      present Age of his son is             = y year

Five years hence,

Age of Jacob will                              = x + 5 year

Age of his son will                                       = y + 5year

Given that the age of Jacob will be three times that of his son

x + 5    =3(y+5)

Add 5 both side we get

x         = 3y + 15 - 5

x          = 3y + 10                    … (1)

 Five years ago,

Age of Jacob will                              = x - 5 year

Age of his son will                                       = y - 5year

 Jacob’s age was seven times that of his son

x – 5    = 7(y -5)

Plug the value of x from equation (1)  we get

3y + 10 – 5     = 7 y – 35

3y + 5             = 7y – 35

3y – 7 y          = - 35 – 5

-4y     =  - 40

y         = - 40 / - 4

y          = 10 year

Plug the value of y in equation first we get

x          = 3* 10 + 10

x          = 40 years

Answer is

Present age of Jacob = 40 years

Present age of his son = 10 years