Question

The ages of Father and his son are in ratio 4:1 . After 4 years, their ratio will be 3:1 . Find their present ages respectively​

Answer 1

➛ Let the ratio of their ages be x.

______________________________

Then,

• Father's age = 4x
• Son's age = x

⠀

After 4 years

• Father's age = 4x + 4
• Son's age = x + 4

⠀

According to the question

⠀

$\tt{\longrightarrow{\dfrac{4x + 4}{x + 4} = \dfrac{3}{1}}}$

⠀

$\tt{\longrightarrow{4x + 4 = 3(x + 4)}}$

⠀

$\tt{\longrightarrow{4x + 4 = 3x + 12}}$

⠀

$\tt{\longrightarrow{4x - 3x = 12 - 4}}$

⠀

$\tt{\longrightarrow{x = 8}}$

⠀

By putting the value of x

• Father's age = 4x = 32
• Son's age = x = 8

⠀

Hence,

• Father's present age is 32 years.
• Son's present age is 8 years.

━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Given : The ages of Father and his son are in the ratio 4 : 1. After 4 years, their ratio will be 3 : 1.

To Find : Their present ages.

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀____________________

Put k in the present age ratio.

$\:$

• Father's present age ratio = 4k
• Son's present age ratio = k

$\: \:$

Add 4 to both.

$\: \:$

• Father's age ratio = (4k + 4)
• Son's age ratio = (x + 4)

$\:$

☯︎ It is also given that, after 4 years their ratio will be 3 : 1

$\: \:$

$\bold{\underline{According \: to \: the \: question \: : }} \:$

$\:$

$\sf:\implies \: \dfrac{(4k + 4)}{(k + 4)} = \dfrac{3}{1} \\ \\ \\ \sf:\implies \: 4k + 4 = 3(x + 4) \\ \\ \\ \sf:\implies \: 4k + 4 = 3k + 12 \\ \\ \\ \sf:\implies \: 4k - 3k = 12 - 4 \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{k = 8}}} \: \bigstar$

$\: \:$

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀____________________

Now,

$\: \:$

• Present age of Son = k = 8 years
• Present age of Father = 4k = 32 years

$\: \:$

$\sf\therefore{\underline{Hence, \: the \: present \: ages \: of \: son \: and \: father \: are \: \bold{8} years \: and \: \bold{32} years \: respectively. }}$