Problems on Ages Formulas

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 + 3x) years = 4x years.

Therefore, (4x + 8) = (2/5) (x + 8)

               => 8x + 16 = 5x + 40

               => 3x = 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 = 2x + 4
=> x = 22.

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Problems on Ages:
Formula:                Problems on Ages Formulas
Solved Examples:  Solved Examples: Set 01     Solved Examples: Set 02
Practice Test:         Practice Test: 01     Practice Test: 02