Question

Aman’s age is three times his son’s age. Ten years ago he was five times his son’s
age. Find their present ages.

Answer 1

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

The present ages are - Son = 20 years and Aman = 60 years.

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

Given :

Aman's age = 3 times his son's age

Ten years ago = Aman was five times his son’s age

To find :

Their Present ages

Solution :

⚝ Present Day -

Consider Son's age as x

Aman = 3x

⚝ 10 Years ago -

Son's age = x - 10

Aman's age = 3x - 10

It is given in the question that Ten years ago he was five times his son’s age.

So,

★ $\boxed{\sf{3x - 10 = 5(x - 10)}}$

$\sf{\implies} \: 3x - 10 = 5(x - 10)$

$\sf{\implies} \: 3x - 10 = 5x - 50$

$\sf{\implies} \: 3x - 5x = - 50 + 10$

$\sf{\implies} \: \cancel- 2x = \cancel - 40$

$\sf{\implies} \: x = \dfrac{40}{2}$

$\sf{\implies} \: x = 20$

Son's present age = 20 years

$\rule{300}{1.5}$

★ Value of 3x

$\sf{\implies} \: 20 \times 3$

$\sf{\implies} \: 60$

Aman's present age = 60 years

$\therefore$ The present ages are - Son = 20 years and Aman = 60 years.

$\rule{300}{1.5}$

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

$\sf{\implies} \: 3(20)- 10 = 5(20 - 10)$

$\sf{\implies} \: 60- 10 = 100 - 50$

$\sf{\implies} \:50 = 50$

$\therefore$ The present ages are - Son = 20 years and Aman = 60 years.

Answer 2

$\mathfrak\pink{Solution!}$

Let the age of the son be x years

Age of Aman =3x

Now,

$\red\star\mathfrak\purple{\large{\underline{\underline{Ten \:years\:ago!}}}}$

Age of son= x-10

Age of Aman= 5(x-10)

Therefore, present age of aman= 5x-50

$\mathfrak{Now,}$

3x-10= 5x-50

⟹3x-5x= 40

⟹-2x=-40

⟹x=$\mathfrak{\frac{40}{2}}$

$\mathfrak\red{⟹x=20}$

Now,

$\bold{Age\: of \:Aman= 3x}$

= 3×20

=60 years

$\mathfrak\orange{Verification:-}$

⟹3×20−10=5×(20−10)

⟹60- 10 = 100 -50

⟹50=50