Question

the present age of father is four times age of his son. after 10 years the age of father will become three times the age of his son. find their present ages.

Answer 1

✶ $\bold{\underline{\rm{\pink{Given:-}}}}$

• The present age of father is four times age of his son.
• After 10 years the age of father will become three times the age of his son.

✶ $\bold{\underline{\rm{\purple{To \; Find:-}}}}$

• find their present ages.

✶ $\bold{\underline{\rm{\blue{Solution:-}}}}$

Let the present age of son = x

Therefore his father's age = 4x

$\bold{\underline{\underline{\sf{\green{\dag \; According \; to \; question:-}}}}}$

★ After 10 years,

✶ Age of father will become three times the age of his son.

Now,

$\implies \sf{4x + 10 = 3(x + 10)}$

$\implies \sf{4x + 10 = 3x + 30}$

$\implies \sf{4x - 3x = 30 - 10}$

$\implies \bold{\underline{\underline{\boxed{\sf{\red{20 years}}}}}}$

$\implies$ Present age of son = 20 years

$\implies$ Present age of Father = 4x = 4 × 20 = 80 years

$\rule{200}{2}$

Answer 2

Let us assume that ,

The present age of father and his son be " x " and " y "

Given ,

The present age of father is four times the age of his son

$\sf \Rightarrow y = 4x \: --- \: (i)$

After 10 years , the age of father will become three times the age of his son

$\sf \Rightarrow y + 10 = 3(x + 10) \\ \\ </p><p>\sf \Rightarrow y + 10 = 3x + 30 \\ \\ </p><p>\sf \Rightarrow y = 3x + 20 \: --- \: (ii)$

Put the value of eq (i) in eq (ii) , we get

$\sf \Rightarrow 4x = 3x + 20 \\ </p><p>\sf \Rightarrow x = 20$

Put the value of x = 20 in eq (i) , we get

$\sf \Rightarrow y = 80$

$\therefore{ \underline{ \sf \bold{ \underl{The \: present \: age \: of \: father \: and \: his \: son \: are \: 80 \: and \: 20 \: years }}}}$