Question

A man is 5 times as old as his son in 2 years time he will be four times as old as his son find their present ages​

Answer 1

Answer :-

Present age of son is 6 years and present age of man is 30 years.

Solution :-

Let the present age of son be x

Man's age = 5 times son's age = 5(x) = 5x

In 2 years

Son's age = x + 2

Man's age = 5x + 2

Given that

In two years Man's age = 4 times of son's age in 2 years

⇒ 5x + 2 = 4(x + 2)

⇒ 5x + 2 = 4x + 8

Transpose 2 to RHS

⇒ 5x = 4x + 8 - 2

⇒ 5x = 4x + 6

Transpose 4x to LHS

⇒ 5x - 4x = 6

⇒ x = 6

Present age of son = x = 6 years

Present age of man = 5x = 5(6) = 30 years

Therefore the present age of son is 6 years and present age of man is 30 years.

Verification :-

Let us check

5x + 2 = 4(x + 2)

Substitute their present ages

⇒ 30 + 2 = 4(6 + 2)

⇒ 32 = 4(8)

⇒ 32 = 32

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Ages of Father and Son is 30 and 6 respectively.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

A man is 5 times as old as his son

After 2 years - Man will be 4 times his son

To Find :

Their present Ages

Solution :

Consider the present age of the son as x

Father's age will be 5x as he is 5 times his son's age.

$\rule{300}{1.5}$

Ages after 2 years :

Father's age =

$\implies$ 5x + 2

Son's age =

$\implies$ x + 2

As it is mentioned in the Question, in 2 years ; the Father's age is 4 times his son's age.

★ $\boxed{\sf{5x + 2 = 4(x + 2)}}$

$\sf{\implies} \: 5x + 2 = 4(x + 2)$

$\sf{\implies} \: 5x + 2 = 4x + 8$

$\sf{\implies} \: 5x - 4x = 8 - 2$

$\sf{\implies} \:x = 6$

Son's age is 6 years.

$\rule{300}{1.5}$

★ Value of 5x

$\sf{\implies} \:5 \times 6$

$\sf{\implies} \:30$

Father is 30 years old.

$\therefore$ The Ages of Father and Son is 30 and 6 respectively.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

As we know their present ages, We can add 2 years in their Ages to check if the condition mentioned in the Question matches.

Condition :

• Father is 4 times his son after 2 years

$\sf{\implies} \:30 + 2 = 32$

$\sf{\implies} \:6 + 2 = 8$

$\sf{\implies} \:32 \div 8 = 4$

4 times 8 is 32.

$\therefore$ The Ages of Father and Son is 30 and 6 respectively.