# Problems Based on Ages

### Age

The Time from the birth of someone till date is called age, that is, the age tells us when he was born and how long he lived.

Questions of this chapter are discussed in the context of the age of two persons, in which the relationship between the ages of two in context of before and after some time is shown. Normally these two people are father and son. Generally questions related to the age of both are asked in the examination. In order to solve the questions, the candidates have to calculate the present age of both the persons or a few years ago or a few years later. Candidates also have to find out the sum of ages of both / average age of both.

Hypothesis

1. To calculate a person’s age before x years, deduct from the present age.

Example: If the current age of Rama is 20, then to calculate the age of before 6 years, we will deduct 6 out of 20, i.e. 6 years ago Ram was 14 years old.

2. To calculate a person’s age after x years then add x to the current age of that person.
Example: If the current age of Rama is 20 years, then after 4 years, it will be 20+ 4 i.e., 24 years.

3. The difference of age is always constant between two individuals. That is, if the present age of the son is 25 years less than the current age of the father, it will always be 25 years short.

– Let us see an example of the questions asked in the examination based on the above facts.

Example 1. After five years my father will be 55 years old. Then 8 years ago what was his age?

Solution: My father’s current age = 55 – 5 = 50 years

∴ 8 years preceding their age = 50 – 8 = 42 years.

Example 2. A’s age is twice the age of B. Four years ago, the age of C was twice the age of A. In four years, age of A will be 32 years, then what is the current age of B and C?
(a) 10, 50 (b) 9, 46 (c) 14, 52 (d) 16 , 54

Solution: (c) As, age of A after 4 years = 32 years
∴ Current age = 32 – 4 = 28 years
∴ Current age of B = 28/2 = 14 years (A is twice than B)
∴ Current Age of C = (current age of A – 4) × 2 + 4 = (28 – 4) × 2 + 4 = 52 years