Question

The sum of present ages of a father and his son is 50 years. After 5 years, the age of the father

becomes thrice the age of his son. Find their present ages.​

Answer 1

Answer :

Present age of father is 40 years and present of his son is 10 years.

Given :

• The sum of present ages of a father and his son is 50 years.
• After 5 years, the age of the father becomes thrice the age of his son.

To find :

• Their present ages.

Solution :

Consider,

• Present age of father = x years
• Present age of son = y years

According to the 1st condition :-

• The sum of present ages of father and his son is 50 years.

$\to\sf{x+y=50}$

$\to\sf{x=50-y............(i)}$

According to the 2nd condition :-

• After 5 years, the age of the father becomes thrice the age of his son.

After 5 years,

• Age of father = (x+5) years
• Age of son = (y+5) years

$\to\sf{x+5=3(y+5)}$

• Put x = 50-y from eq (i).

$\to\sf{50-y+5=3y+15}$

$\to\sf{55-y=3y+15}$

$\to\sf{-y-3y=15-55}$

$\to\sf{-4y=-40}$

$\to\sf{y=10}$

★Present age of son = 10 years

★ Present age of father = (50-10) = 40 years

Answer 2

Given :-

• The sum of present ages of a father and his son = 50 years.
• After 5 years the age of the father becomes thrice the age of his son.

To find :-

• Find Their present ages.

Solution :-

Let the pesent age of father = 'x' years

Let the present age of son = 'y' years

1st condition :-

• The sum of present ages of a father and his son = 50 years.

$\implies\rm{x+y=50}$

$\implies\rm{x=50-y \: .....(1)}$

2nd condition :-

• After 5 years the age of the father becomes thrice the age of his son.

So,

• Age of father = (x+5) years.
• Age of son = (y+5) years.

$\implies\rm{x+5=3(y+5)\: .....(2)}$

Put the value of x from equation (1),

$\implies\rm{50-y+5=3y+15}$

$\implies\rm{55-y=3y+15}$

$\implies\rm{-y-3y=15-55}$

$\implies\rm{-4y=-40}$

$\implies\rm{y=10}$

Answer :-

★ Present age of son = 10 years.

★ Present age of father = (50 - 10) = 40 years.