Question

a boy is now one third as old as his father after 12 years he will be half as old as his father. find their present ages

Answer 1

Let the age of Father be x
Age of Boy = 1/3 rd of x = x/3
After 12 years father`s age = x+12
Boy`s age = x/3  + 12
But given that  boy`s age will be half of father`s age = (x+12)/2
⇒ x/3  +12 = (x+12)/2
⇒ (x+36)/3 = (x+12)/2
⇒ 2(x+36) = 3(x+12)
⇒ 2x + 72 = 3x + 36
⇒ 72 -36 = 3x - 2x
⇒ 36 = x
∴ x = 36
∴ Father`s age  = x = 36Yrs
   Boy`s age = x/3 = 36/3 = 12Yrs

Answer 2

Answer:

The present age of father is 36 years and boy is 13 years.

Step-by-step explanation:

Let father's present age be x

Now we are given that a boy is now one third as old as his father

So, Boys' present age = $\frac{x}{3}$

After 12 years ,

Father's age = x+12

Boy's age =  $\frac{x}{3}+12$

Now we are given that after 12 years he will be half as old as his father.

So, $\frac{1}{2}(x+12)=\frac{x}{3}+12$

$\frac{x}{2}+6=\frac{x}{3}+12$

$\frac{x}{2}-\frac{x}{3}=-6+12$

$\frac{3x-2x}{6}=6$

$\frac{x}{6}=6$

$x=36$

Thus the father's present age = 36 years.

Boys' present age = $\frac{36}{3}=12$

Hence the present age of father is 36 years and boy is 13 years.