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

Answer:

Aman is 60 years old and his son is 20 years old.

Step-by-step 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 :

Let the present ages be -

• Son as y
• Aman as 3y

Ages 10 years ago -

• Son = (y - 10)
• Aman = (3y - 10)

$\rule{300}{1.5}$

According to the question,

Aman was 5 times his son's age 10 years ago.

$\rm{\longrightarrow} \: 5(y - 10) = 3y - 10 \\ \\ \rm{\longrightarrow} \: 5y - 50 = 3y - 10 \\ \\ \rm{\longrightarrow} \: 5y - 3y = - 10 + 50 \\ \\ \rm{\longrightarrow} \: 2y = 40 \\ \\ \rm{\longrightarrow} \: y = \dfrac{40}{2} \\ \\ \rm{\longrightarrow} \: y = 20$

Son's present age = 20 years old

$\rule{300}{1.5}$

★ Aman's present age -

$\rm{\longrightarrow} \: 3(20) \\ \\ \rm{\longrightarrow} \: 60$

Aman's present age = 60 years old

$\therefore$ Aman is 60 years old and his son is 20 years old.

Answer 2

❥${\underline{\underline{\huge{\mathtt{Question:-}}}}}$

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.

❥${\underline{\underline{\huge{\mathtt{Solution:-}}}}}$

Given:- Aman's age is 3 times of his son's age and 10 years ago he was 5 times of his son's age.

Consider,

•${\green{\bold{Aman's\:son's\: present\:age = x\: years}}}$

•${\blue{\bold{Aman's\: present\:age = 3x\: years}}}$

10 years ago,Aman's son's age=${\red{\bold{(x-10)\: years}}}$

10 years ago,Aman's age = ${\purple{\bold{(3x-10)\: years}}}$

According to the question,

5(x-10)=3x-10

→ 5x - 50=3x-10

→5x - 3x = -10+50

→ 2x = 40

→ x = 20

${\red{\boxed{\bold{Aman's\:son's\: present\:age=20\: years}}}}$

${\purple{\bold{Aman's\:present\:age=(3×20)\: years}}}$

= 60 years

${\red{\boxed{\bold{Aman's\: present\:age=60\: years}}}}$

❥${\underline{\underline{\huge{\mathtt{Answer:-}}}}}$

Aman's present age is 60 years and his son's present age is 20 years.