The LCM of two numbers is 20 times their HCF. The sum of HCF and LCM is 2520. If one of the numbers is 480, the other number is

Options

A. 400
B. 480
C. 520
D. 600

Answer

To solve the problem step by step, we will follow the given information and use the relationships between HCF (Highest Common Factor) and LCM (Lowest Common Multiple).

### Step-by-Step Solution:

1. **Understanding the Relationships**:
- We know that the LCM of two numbers is 20 times their HCF.
- Let the HCF of the two numbers be \( x \).
- Therefore, the LCM can be expressed as \( 20x \).

2. **Setting Up the Equation**:
- The sum of HCF and LCM is given as 2520.
- Thus, we can write the equation:
\[ x + 20x = 2520 \]

3. **Simplifying the Equation**:
- Combine like terms:
\[ 21x = 2520 \]

4. **Solving for HCF**:
- To find \( x \), divide both sides of the equation by 21:
\[ x = \frac{2520}{21} \]
- Calculating this gives:
\[ x = 120 \]
- So, the HCF is 120.

5. **Finding the LCM**:
- Now, substitute \( x \) back into the expression for LCM:
\[ \text{LCM} = 20x = 20 \times 120 = 2400 \]

6. **Using the HCF and LCM to Find the Other Number**:
- We use the relationship:
\[ \text{HCF} \times \text{LCM} = \text{First Number} \times \text{Second Number} \]
- Here, we know one number is 480, so we can set up the equation:
\[ 120 \times 2400 = 480 \times \text{Other Number} \]

7. **Calculating the Other Number**:
- First, calculate \( 120 \times 2400 \):
\[ 120 \times 2400 = 288000 \]
- Now, we can rearrange the equation to find the other number:
\[ \text{Other Number} = \frac{288000}{480} \]
- Performing the division gives:
\[ \text{Other Number} = 600 \]

### Conclusion:
The other number is **600**.