**Important Formulas on "Problems on Ages”:**- 1. If the current age is ‘
*x’*, then ‘*n’*times the age is ‘*nx’*. - 2. If the current age is
*x*, then age*n*years later/hence = (*x*+*n)*. - 3. If the current age is ‘
*x’*, then age ‘*n’*years ago = (*x*-*n)*. - 4. The ages in a ratio ‘
*a*:*b’*will be ‘*ax’*and ‘*bx’*. - 5. If the current age is
*x*, then 1/n of the age is*x/n.*

__Example. 01__**A father was 4 times as old as his son 8 years ago. Eight years hence, father will be twice as old as his son. Find their present ages.**

__Solution:__
Let son's age 8 years ago be x years.

Thus, father's age at that time = 4x years

After 8 years, son's age = (x + 8) + 8 = (x+16) years

After 8 years, father's age = (4x + 8) + 8 = (4x+16) years

So, According to Question, 2(x + 16) = 4x + 16 or x = 8

Therefore, The present age of the son = x + 8 = 16 years

The present age of the father = 4x + 8 = 32 + 8= 40 years

__Example. 02__**Father is aged three times more than his son. After 8 years, he would be two and a half times of his son's age. After further 8 years, how many times would he be of his son's age?**

__Solution:__
Let Son's present age be ‘

*x’*years.
Then, father's present age =(

*x*+ 3*x*) years = 4*x*years.
Therefore, (4

*x*+ 8) = (2/5) (*x*+ 8)
=> 8

*x*+ 16 = 5*x*+ 40
=> 3

*x*= 24 =>*x*= 8.
After further 8 years, Son's age will be (x + 16) = 24 years.

And father's age will be (4x +16) = 48 years.

Hence, the required ratio is (4x +16)/(x+16) = 48/24 = 2.

__Example. 03__**A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:**

(A) 14 years

(B) 18 years

(C) 20 years

(D) 22 years

Answer:
Option D

__Solution:__
Let the
son's present age be

*x*years. Then, man's present age = (*x*+ 24) years.
∴ (

*x*+ 24) + 2 = 2(*x*+ 2)
=>

=>

*x*+ 26 = 2*x*+ 4=>

*x*= 22.**Problems on Ages: Next Tests:**