Question

The father 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

Let the age of father=x
   the age of the son=y
according to 1st condition
       x=2y  -----1)
according to 2nd condition 
    x-20=12(y-20)
    x-20=12y-240----2)
from 1) eq. 2) becomes
2y-20=12y-240
10y=220
y=22 years

Answer 2

Given,

• The Father is Twice as old as his son .
• 20 years ago , the age of the father was 12 times the age of the son.

To Find,

• The Present Age

Solution,

⇒Suppose the Present age of the son be x

And, Suppose the Present age of the Father be y

According to the First Condition :-

• The Father is Twice as old as his son .

$\implies \boxed{\sf{y = 2x}}$

According to the Second Condition :-

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

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

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

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

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

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

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

$\implies \sf{x = \dfrac{220}{10}}$

$\implies \boxed{\bold{x = 22 \ years}}$

Now Put the value of x in First Condition :-

$\implies \sf{y = 2x}$

$\implies \sf{y = 2 \times 22}$

$\implies \boxed{\bold{y = 44 \ years}}$

Therefore,

$\boxed{\sf{\red{Age \ of \ the \ Father = y = 44 \ years}}}$

$\boxed{\sf{\red{Age \ of \ the \ Son = x = 22 \ years}}}$

$\rule{200}2$