Hello guys as we all know that word problem consisting of linear equation are hard to solve when we were in schools and especially problems on ages. At some point of our schooling we felt that why these chapter is in syllabus. But at later stage of life we find out that these is the most important topic because every competitive exam has quantitative aptitude section and it consists of age problems. Hence we are here to share some basic concepts that will help in solving age problems.

**Basic Concepts**

- If the present age of ‘P’ is ‘x’ years, then ‘n’ years ago = Age of ‘P’ was
**(x-n) years**. - If the present age of ‘P’ is ‘x’ years, then ‘n’ years after = Age of ‘P’ was
**(x+n) years**. - In general we have to assume the present age of one person. it is good to assume present age as
**x years**. - If the present age of you and your friend is ‘x’ and ‘y’ years respectively then
**‘n’ years ago**age of you and your friend were**(x-n) and (y-n) year**s respectively or**‘n’ years****after**from the present age will be**(x+n) and (y+n) years**respectively. - The age difference between you and your friend will remain same throughout your lifetime because clock will run equally for both of you.

**Some Examples :-**

**Example :- Pradeep’s age after 15 years will be 5 times his age 5 years back. What is the present age of Pradeep ?**

Suppose Pradeep’s present age be x years. Then

Pradeep’s age after 15 years will be (x+15) years.

Pradeep’s age 5 years ago was (x-5) years.

According to question x+15 = 5(x-5)

x+15 = 5x-25

4x = 40

x = 10

**Hence Pradeep’s present age = 10 years.**

**Example :- One year ago, the ratio of Dhoni’s and Virat’s age was 6:7 respectively.Four years hence, this ratio would become 7:8. How old is Virat ?**

Suppose Dhoni’s and Virat ages one year ago be 6x and 7x years respectively. Then,

Dhoni’s age 4 years hence = (6x+1)+4 = 6x+5 years

Virat’s age 4 years hence = (7x+1)+4 = 7x+5 years

**(****Note**** :- We have added one because the age we had assumed is for 1 year ago)**

(6x+5)/(7x+5) = 7/8

8(6x+5) = 7(7x+5)

48x+40 = 49x+35

x = 5

**Hence Virat’s present age is (7x+1) = 7*5 + 1 = 36 years.**

**Example :- The ages of two persons differ by 16 years. If 6 years ago, the elder one be 3 times as old as the younger one, find their present ages.**

Let the age of the younger one be x years.

Then, age of elder person = x+16 (According to question)

3(x-6) = (x+16-6)

3x-18 = x+10

2x = 28

x = 14

**Hence there present ages are 14 years and (14+16) = 30 years.**

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This topic has been asked by our reader **Pradeep singh tomar **thats why his name is used in first example. Any doubts then write it down in the comment box below.

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