LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

SIMULTANEOUS LINEAR EQUATION - PROBLEM ON AGE

**Problem On Ages –**

**Example.1) Five years ago, a man was
seven times as old as his son, while 5 years hence, the man will be 3 times as
old as his son. Find their personal ages.**

**Ans.) Let, the
present ages of the man and his son be x years and y years respectively.**

**Man’s age 5 years ago = (x – 5) years**

**Son’s age 5 years ago would be = (y – 5) years**

** So, (x – 5) = 7(y – 5)**

** Or, x – 7y = 5 – 35
**

** Or, x – 7y = - 30
…………….(i)**

**Man’s age 5 years hence = (x + 5) years**

**Son’s age 5 years hence = (y + 5) years**

**As per the given condition –**

** (x + 5) =
3 (y + 5)**

** => x – 3y =
15 – 5**

** => x – 3y =
10 ………………(ii)**

**On subtracting (i) from (ii), we get –**

** x
– 7y = - 30**

** x
– 3y = 10**

** ------------------**

**
- 4y = - 40**

** => y = 10 **

**Now we will substitute the value of y in (i), and we find –**

** x
– 7y = - 30**

** or, x – (7 X 10) = - 30**

** or, x
= 70 – 30 **

** or, x
= 40 **

**So, hence the man’s present age is 40 years and son’s
present age is 10 years. (Ans.)**

**Example.2) The present age of a woman is 3 years more
than 3 times the age of her daughter, three years hence, the woman’s age will
be 10 years more than twice the age of her daughter. Find their present ages.**

**Ans.) Let the present
ages of the woman and her daughter be ‘x’ years and ‘y’ years respectively.
Then,**

**As per the given condition –**

** x = 3y + 3**

** => x – 3y = 3
………………..(i)**

**And, as per the given condition –**

** (x + 3)
= 2y + 10 **

** => x – 2y = 10
– 3 **

** => x – 2y = 7
……………………(ii)**

**Now, we will subtract (i) from (ii), and will get –**

** x
– 2y = 7**

** x
– 3y = 3**

** ---------------**

** y = 4**

**Now, we will substitute the value of y, in (i) and we will
get –**

** x – 3y =
3**

** => x – (3 X 4) = 3**

** => x – 12 =
3**

** => x = 15**

**Hence, the present age of woman would be 15 years and the
age of daughter would be 4 years. (Ans.)**