IF HCF and LCM of two numbers are 5 and 485. If sum of both numbers is 100 find difference bwtween then.

Answer

To solve the problem, we need to find the difference between two numbers given their HCF, LCM, and their sum. Let's break it down step by step.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- HCF (Highest Common Factor) = 5
- LCM (Lowest Common Multiple) = 485
- Sum of the two numbers = 100

2. **Let the Two Numbers be:**
- Let the first number be \( x \).
- The second number will then be \( 100 - x \) (since their sum is 100).

3. **Use the Relationship Between HCF, LCM, and the Two Numbers:**
- The relationship states that:
\[ \text{HCF} \times \text{LCM} = \text{First Number} \times \text{Second Number} \]
- Substituting the known values:
\[ 5 \times 485 = x \times (100 - x) \]

4. **Calculate the Product of HCF and LCM:**
- Calculate \( 5 \times 485 \):
\[ 5 \times 485 = 2425 \]
- Therefore, we have:
\[ 2425 = x \times (100 - x) \]

5. **Set Up the Equation:**
- Expanding the right-hand side:
\[ 2425 = 100x - x^2 \]
- Rearranging gives:
\[ x^2 - 100x + 2425 = 0 \]

6. **Factor the Quadratic Equation:**
- We need to factor \( x^2 - 100x + 2425 \).
- We look for two numbers that multiply to 2425 and add up to 100. These numbers are 45 and 55.
- Thus, we can factor the equation as:
\[ (x - 45)(x - 55) = 0 \]

7. **Find the Values of \( x \):**
- Setting each factor to zero gives:
\[ x - 45 = 0 \quad \Rightarrow \quad x = 45 \]
\[ x - 55 = 0 \quad \Rightarrow \quad x = 55 \]

8. **Determine the Two Numbers:**
- The two numbers are 45 and 55.

9. **Calculate the Difference Between the Two Numbers:**
- The difference is:
\[ |55 - 45| = 10 \]

### Final Answer:
The difference between the two numbers is **10**.