Question

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

Answer 1

${\huge{\mathcal{\underline{\underline{\star{ANSWER{\star}}}}}}}$

Ages Before 2 years be son as x and father as 5x

Four years later it will be son as x + 4 and father as 5x + 4

==> 3(x + 4) + 8 = 5x + 4

==> 3x + 20 = 5x + 4

==> 3x - 5x = 4 - 20

==> 2x = 16

==> x = 8

Son = x + 2 = 8 + 2 = 10 Years

Father = 5x + 2 = 40 + 2 = 42 Years

.°. The son is 10 Years old and father is 42 Years old.

Answer 2

Answer:

The present ages of Father and son are 42 Years and 10 Years respectively.

Step-by-step explanation:

Given :

• Two ears ago = father was five times as old as son
• Two years later = father age will be 8 more than three times the age of his son.

To Find :

• Find their present ages.

Solution :

✯ $\textbf{\small{\underline{Let the Ages two years ago as -}}}$

• Son as x
• Father as 5x

$\rule{300}{1.5}$

✯ $\textbf{\small{\underline{Present ages - }}}$

• Son --> x + 2
• Father --> 5x + 2

$\rule{300}{1.5}$

✯ $\textbf{\small{\underline{Ages after two years -}}}$

• Son --> x + (2 + 2)
• Father --> 5x + (2 + 2)

$\rule{300}{1.5}$

✯ $\textbf{\small{\underline{According to the Question -}}}$

Two years later, father age will be 8 more than three times the age of his son.

★ $\boxed{5x + (2+2)= 8 + 3(x + 4) }$

$\longrightarrow \: 5x + (2 + 2) = 8 + 3(x + 4)$

$\longrightarrow \: 5x + 4 = 8 + 3x + 12$

$\longrightarrow \: 5x + 4 = 3x + 20$

$\longrightarrow \: 5x - 3x= 20 - 4$

$\longrightarrow \:2x= 16$

$\longrightarrow \:x= \dfrac{16}{2}$

$\longrightarrow \:x = 8 \: .....\textbf{[ Son's age before 2 years ]}$

$\rule{300}{1.5}$

★ Value of (x + 2)

$\longrightarrow \: 8 + 2$

$\longrightarrow \: 10$

Son's present age = 10 Years

$\rule{300}{1.5}$

★ Value of 5x + 2

$\longrightarrow \: 5(8) + 2$

$\longrightarrow \: 40 + 2$

$\longrightarrow \: 42$

Father's present age = 42 years

$\therefore$ The present ages of Father and son are 42 Years and 10 Years respectively.

$\rule{300}{1.5}$

Verification :-

As mentioned in the Question, two years later, father's age will be 8 more than three times the age of his son.

✯ $\textbf{\small{\underline{Present Ages -}}}$

• Father = 42
• Son = 10

✯ $\textbf{\small{\underline{Ages after 2 years -}}}$

• Father = 42 + 2 --> 44
• Son = 10 + 2 --> 12

$\longrightarrow \: 44 = 8 + 3(12)$

$\longrightarrow \: 44 = 8 + 36$

$\longrightarrow \: 44 = 44$

$\therefore$ The present ages of Father and son are 42 Years and 10 Years respectively.