Question

5 years ago a man was 5 times the age of the son .10 years hence the man age will be double the age of the son . find there present age​

Answer 1

Given :

• 5 years ago a man was 5 times the age of the son.

• 10 years hence the man age will be double the age of the son

To Find :

• Their present ages.

Solution :

5 years ago :

Son's age = x and father's age = 5x

Present ages :

Son's age = x + 5 and father's age = (5x+5)

10 years hence :

Son's age = 2(x+5+10) and father's age = (5x+5+10)

According to the Question :

→ 2(x+5+10) = 5x + 5 + 10

→ 2x + 10 + 20 = 5x + 15

→ 2x + 30 = 5x + 15

→ 2x - 5x = 15 - 30

→ -3x = -15

→ x = -15/-3

→ x = 5 years

_______________

★ Present age of son = (5+5) = 10 years

★ Present age of father = 5(5)+5 = 30 years

Answer 2

Answer:

• Father is Fives times of Son, then Ratio of Father to Son is 5 : 1
• Father is Double of Son, then Ratio of Father to Son will be 2 : 1

$\underline{\bigstar\:\textsf{According to the Question :}}$

⠀⠀⠀⠀+ 5 yrs⠀⠀⠀⠀⠀⠀⠀ + 10 yrs

Past ────── Present ────── Future

F : S⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀F : S

5 : 1⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀2 : 1

Let the Past Ratio be 5n and n respectively

$:\implies\sf\dfrac{Father + 5\:yrs + 10\:yrs}{Son+5\:yrs+10\:yrs}=\dfrac{2}{1}\\\\\\:\implies\sf \dfrac{5n + 15\:yrs}{n+15\:yrs}=\dfrac{2}{1}\\\\\\:\implies\sf 5n + 15\:yrs = 2(n + 15\:yrs)\\\\\\:\implies\sf 5n + 15\:yrs = 2n + 30\:yrs\\\\\\:\implies\sf 5n-2n = 30\:yrs-15\:yrs\\\\\\:\implies\sf 3n = 15\:yrs\\\\\\:\implies\sf n=\dfrac{15\:yrs}{3}\\\\\\:\implies\underline{\boxed{\sf n=5\:yrs}}$

$\rule{150}{1}$

$\underline{\bigstar\:\textsf{Present Age :}}$

$\bullet\:\:\textsf{Son = n + 5 = 5 + 5 = \textbf{10 years}}\\\bullet\:\:\textsf{Father = 5n + 5 = 5(5) + 5 = \textbf{30 years}}$

⠀

$\therefore$ Present Age of Son & Father is 10 years & 30 years respectively.