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.
