The LCM of two numbers is 20 times of their HCF and (LCM + HCF) = 2520. If one number is 480, what will be the triple of another number?

Options

A. 1200
B. 1500
C. 2100
D. 1800

Answer

To solve the problem step by step, we will follow the information provided in the question:

1. **Understanding the relationship between LCM and HCF**:
We know that the LCM of two numbers is 20 times their HCF. Let's denote the HCF as \( X \). Therefore, the LCM can be expressed as:
\[ \text{LCM} = 20X \]

2. **Using the sum of LCM and HCF**:
We are also given that the sum of the LCM and HCF is 2520:
\[ \text{LCM} + \text{HCF} = 2520 \]
Substituting the expression for LCM:
\[ 20X + X = 2520 \]
This simplifies to:
\[ 21X = 2520 \]

3. **Solving for HCF (X)**:
To find \( X \), we divide both sides by 21:
\[ X = \frac{2520}{21} = 120 \]
So, the HCF is 120.

4. **Finding the LCM**:
Now, we can find the LCM using the value of \( X \):
\[ \text{LCM} = 20X = 20 \times 120 = 2400 \]

5. **Using the relationship between HCF, LCM, and the two numbers**:
We know that for two numbers \( a \) and \( b \):
\[ \text{HCF} \times \text{LCM} = a \times b \]
Given that one number \( a = 480 \), we can substitute the values:
\[ 120 \times 2400 = 480 \times b \]

6. **Calculating the other number \( b \)**:
First, calculate \( 120 \times 2400 \):
\[ 120 \times 2400 = 288000 \]
Now, we can solve for \( b \):
\[ 288000 = 480 \times b \]
Dividing both sides by 480:
\[ b = \frac{288000}{480} = 600 \]

7. **Finding the triple of the other number**:
Finally, we need to find the triple of the other number \( b \):
\[ 3 \times 600 = 1800 \]

Thus, the answer is that the triple of the other number is **1800**.