Question

The present age of a son is half the present age of his father. Ten years ago, the father was thrice as old as his son. What are their present ages?

P.s. Pls give working also

Answer 1

Answer :-

Present ages of father and son are 40 years and 20 years resepectively.

Explanation :-

Let the present age of father be 'x' years

Present age of a son = Half the present age of his father = (1/2) * x = x/2 years

Age of father ten years ago = (x - 10) years

Age of son ten years ago = {(x/2) - 10} years

Given

Age of fathe ten years ago = thrice the Age of son ten years ago

⇒ (x - 10) = 3{ (x/2) - 10 }

⇒ x - 10 = 3 { (x - 20)/2 }

⇒ x - 10 = 3(x - 20)/2

⇒ 2(x - 10) = 3(x - 20)

⇒ 2x - 20 = 3x - 60

⇒ - 20 + 60 = 3x - 2x

⇒ 40 = x

⇒ x = 40

i.e Present age of father = x = 40 years

Present age of son = (x/2) = (40/2) = 20 years

∴ Present ages of father and son are 40 years and 20 years resepectively.

Answer 2

$\LARGE{\sf{==== \: Answer \:====}}$

Assuming :-

Let the present age of father be 'a'.

So, the present age of son be 'a/2'.

Solution :-

Age of father ten years ago = (a - 10)

So, Age of son ten years ago = (a - 10)/2.

» A. T. Q

(a - 10) = 3[(a/2) - 10]

________[Taking L.C.M]__________

a - 10 = 3 [(a - 20)/2]

a - 10 = 3(a - 20)/2

2(a - 10) = 3(a - 20)

2a - 20 = 3a - 60

- 20 + 60 = 3a - 2a

40 = a

$\LARGE{\boxed{\boxed{\sf{\red{Age \: of \: Father \: = \: 40 \: yrs}}}}}$

$\rule{200}{2}$

Age of son = 40/2

$\LARGE{\boxed{\boxed{\sf{\red{Age \: of \: Son \: = \: 20 \: yrs}}}}}$