Certainly! Let's solve this problem step by step.
1. Establish the Variables:
- Let the present age of Rahul be [tex]\( 5x \)[/tex].
- Let the present age of Haroon be [tex]\( 7x \)[/tex].
Here, [tex]\( x \)[/tex] is a variable representing a common multiplier for their ages.
2. Future Ages:
- Four years from now, Rahul's age will be [tex]\( 5x + 4 \)[/tex].
- Four years from now, Haroon's age will be [tex]\( 7x + 4 \)[/tex].
3. Sum of Future Ages:
- According to the problem, four years from now, the sum of their ages is 56 years. Therefore, we can write the equation:
[tex]\[
(5x + 4) + (7x + 4) = 56
\][/tex]
4. Simplify the Equation:
- Combine the terms on the left side of the equation:
[tex]\[
5x + 7x + 4 + 4 = 56
\][/tex]
[tex]\[
12x + 8 = 56
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
- Subtract 8 from both sides of the equation to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
12x + 8 - 8 = 56 - 8
\][/tex]
[tex]\[
12x = 48
\][/tex]
- Divide both sides by 12 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 4
\][/tex]
6. Find Their Present Ages:
- Now that we have [tex]\( x \)[/tex], we can find the present ages:
- Rahul's age is [tex]\( 5x = 5 \times 4 = 20 \)[/tex] years.
- Haroon's age is [tex]\( 7x = 7 \times 4 = 28 \)[/tex] years.
So, the present ages are:
- Rahul is 20 years old.
- Haroon is 28 years old.
