Question

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?

Answer 1

Let Jacobs age be x and his son’s age be y.

Five years hence(later),

x+ 5 = 3 (y + 5)

$\Rightarrow$ x+ 5 = 3 y + 15

$\Rightarrow$ x - 3 y = 10.......(1)

Also, five years ago(before),

x-5 = 7 (y – )5

$\Rightarrow$ x-5 = 7y – 35

$\Rightarrow$ x-7y = -30........(2)

Subtracting equation (2) from (1),

x - 3 y = 10

-x +7y = 30 ($\because$ eq.(2) changes its sign)

4y = 40

$\because$ 4 y = 40

$\therefore$ y = 10

Put y = 10 in eq. (1),

x - 3(10) = 10 $\Rightarrow$ x - 30 = 10

$\Rightarrow$ x = 40

Thus, present age of Jacob=x=40 years and

present age of Jacob's son=y=10 years.