Question

a father is five times as old as his son.after 24 yrs he will be twice as old as his son. the present age of the father is .............. pls answer
​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

$\:\:$

• Father is five times as old as his son

• After 24 years he will be twice as old as his son

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

$\:\:$

• Their present ages

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

$\:\:$

• Let the father's present age be "f"

• Let the son's present age be "s"

$\:\:$

$\underline{\bold{\texttt{Father's age after 24 years :}}}$

$\:\:$

➜ f + 24 ⚊⚊⚊⚊ ⓵

$\:\:$

$\underline{\bold{\texttt{Son's age after 24 years :}}}$

$\:\:$

➜ s + 24 ⚊⚊⚊⚊ ⓶

$\:\:$

Given that , father is five times as old as his son

$\:\:$

So,

$\:\:$

➜ f = 5s ⚊⚊⚊⚊ ⓷

$\:\:$

Also given that , after 24 years he will be twice as old as his son

$\:\:$

From ⓵ & ⓶

$\:\:$

➜ f + 24 = 2(s + 24)

$\:\:$

➜ f + 24 = 2s + 48

$\:\:$

➜ f - 2s = 48 - 24

$\:\:$

➜ f - 2s = 24 ⚊⚊⚊⚊ ⓸

$\:\:$

⟮ Putting f = 5s from ⓷ to ⓸ ⟯

$\:\:$

➜ f - 2s = 24

$\:\:$

➜ 5s - 2s = 24

$\:\:$

➜ 3s = 24

$\:\:$

➜ $\sf s = \dfrac { 24 } { 3 }$

$\:\:$

➨ s = 8 ⚊⚊⚊⚊ ⓹

$\:\:$

• Hence the present age of son is 8 years

$\:\:$

⟮ Putting s = 8 from ⓹ to ⓷ ⟯

$\:\:$

➜ f = 5s

$\:\:$

➜ f = 5(8)

$\:\:$

➨ f = 40

$\:\:$

• Hence the present age of father is 40 years

$\:\:$

∴ The present ages of father and son are 40 years & 8 years respectively