Question

Two years ago, father was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son. Find the present ages of father and son.

Answer 1

Given :-

• 2 years ago, father was 5 times as old as his son.
• 2 years later , his age will be 8 more than 3 times 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 :-

• 2 years ago, father was 5 times as old as his son.

2 years ago,

• Age of father = (x-2) years
• Age of son = (y-2) years

$\to\sf{x-2=5(y-2)}$

$\to\sf{x-2=5y-10}$

$\to\sf{x=5y-8.............(1)}$

According to the 2nd condition :-

• 2 years later , his age will be 8 more than 3 times the age of his son.

2 years later,

• Age of father = (x+2) years
• Age of son = (y+2) years

$\to\sf{x+2=3(y+2)+8}$

$\to\sf{x+2=3y+6+8}$

$\to\sf{x+2=3y+14}$

$\to\sf{5y-8+2=3y+14\:[put\:x=5y-8\: from\:eq(1)]}$

$\to\sf{5y-6=3y+14}$

$\to\sf{5y-3y=14+6}$

$\to\sf{2y=20}$

$\to\sf{y=10}$

• Present age of son = 10 years

Now , put y = 10 in eq (1) .

$\to\sf{x=5y-8}$

$\to\sf{x=5\times\:10-8}$

$\to\sf{x=42}$

• Present age of father = 42 years

Answer 2

★${\underline{\underline{\large{\bold{Given:-}}}}}$

• 2 years ago, father was 5 times as old as his son.
• 2 years later, his age will be 8 more than 3 times the age of his son.

★${\underline{\underline{\large{\bold{To\:Find:-}}}}}$

• Present age of father.
• Present age of son.

★${\underline{\underline{\large{\bold{Solution:-}}}}}$

Let ,

• Father's present age = m years
• Son's present age = n years

${\underline{\sf{According\: to\:the\: first\: condition:-}}}$

${\boxed{\sf{Father's\:age(2\: years\:ago)=5\times\: Son's\: age (2\: years\:ago)}}}$

$\mapsto\sf{(m-2)=5(n-2)}$

$\mapsto\sf{m-2=5n-10}$

$\mapsto\sf{m=5n-8...............(i)}$

${\underline{\sf{According\: to\:the\: second\: condition:-}}}$

${\boxed{\sf{Father's\:age(2\: years\: later)=3\times\: Son's\: age+8 (2\: years\: later)}}}$

$\mapsto\sf{(m+2)=3(n+2)+8}$

$\mapsto\sf{m+2=3n+6+8}$

$\mapsto\sf{5n-8+2=3n+14}$

$\mapsto\sf{2n=20}$

$\mapsto\sf{n=10}$

★ Present age of son = 10 years

★ Present age of father = 5×10-8 = 42 years