Question

A father is twice as old
or is twice as old as his son. 20 years ago, the age
Of the father was 12 times the age of the son. The present
age of the son is? ​

Answer 1

Answer:

Present age of the son = x

Present age of the father = 2x

Age of the son 20 years ago = x - 20

Age of the father 20 years ago = 2x - 20

2x - 20 = 12 ( x - 20 )

2x - 20 = 12x - 240

2x - 12x = -240 + 20

-10x = -220

x = 220/10 = 22

Therefore, present age of the son is 22 years and present age of the father is ( 22 *2 ) = 44 years.

Answer 2

Let us assume that the present age of the son be x years.

A father is twice as old as his son.

$\small{\sf{\:\:\:\:\:\:\:\:\:{\underline{As\:per\:given\:condition}}}}$

Age of father = 2 × Age of son

$\implies\:\sf{Age\:of\:father\:=\:2x}$

20 years ago, the age of the father was 12 times the age of the son.

20 years ago, the age of son = (x - 20) years

And age of father = (2x - 20) years

$\small{\sf{\:\:\:\:\:\:\:\:\:{\underline{As\:per\:given\:condition}}}}$

20 years ago, age of father = 12 × (Age of son, 20 years ago)

$\implies\:\sf{2x-20\:=\:12(x-20)}$

$\implies\:\sf{2x-20\:=\:12x-240}$

$\implies\:\sf{2x-12x\:=\:-240+20}$

$\implies\:\sf{-10x\:=\:-220}$

$\implies\:\sf{x\:=\:\frac{-220}{-10}}$

$\implies\:\sf{x\:=\:22}$

Therefore, the present age of the son is 22 years.

Now, substitute value of x in of father.

Age of father = $\sf{2(22)\:=\:44}$

Therefore, the present age of a father is 44 years.