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SIMPLE EQUATIONS

The age of Abhijit is four times that of his son Amit. If the difference in their ages is 36 years, find the age of Amit.


Sagot :

Certainly! Let's solve this step-by-step.

1. Define Variables:
Let Amit's age be [tex]\( x \)[/tex].

2. Express Abhijit's Age:
According to the problem, Abhijit's age is four times Amit's age. So, Abhijit's age would be [tex]\( 4x \)[/tex].

3. Set Up the Equation:
The difference between Abhijit's age and Amit's age is given as 36 years. Therefore, we can set up the following equation:
[tex]\[ 4x - x = 36 \][/tex]

4. Simplify the Equation:
Combine like terms on the left side of the equation:
[tex]\[ 3x = 36 \][/tex]

5. Solve for [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], divide both sides of the equation by 3:
[tex]\[ x = \frac{36}{3} \][/tex]
[tex]\[ x = 12 \][/tex]
So, Amit's age is 12 years.

6. Find Abhijit's Age:
Now that we know Amit's age, we can find Abhijit's age by substituting [tex]\( x \)[/tex] into the expression for Abhijit's age:
[tex]\[ 4x = 4 \times 12 = 48 \][/tex]
Therefore, Abhijit's age is 48 years.

Summary:
- Amit's age is 12 years.
- Abhijit's age is 48 years.