LCM of two numbers is 16 times the HCF. The sum of LCM and HCF is 850 and one number is 125, so what is the second number?

Options

A. 320
B. 355
C. 390
D. 260

Answer

To solve the problem step by step, let's break down the information given and apply the relevant mathematical concepts.

### Step-by-Step Solution:

1. **Define Variables:**
- Let the HCF (Highest Common Factor) be \( x \).
- According to the problem, the LCM (Lowest Common Multiple) is \( 16 \times x \).

2. **Sum of LCM and HCF:**
- The sum of LCM and HCF is given as 850. Therefore, we can write the equation:
\[ x + 16x = 850 \]
- This simplifies to:
\[ 17x = 850 \]

3. **Solve for HCF:**
- To find \( x \), divide both sides of the equation by 17:
\[ x = \frac{850}{17} = 50 \]
- So, the HCF is \( 50 \).

4. **Calculate LCM:**
- Now, substitute \( x \) back into the equation for LCM:
\[ \text{LCM} = 16 \times x = 16 \times 50 = 800 \]

5. **Use the Relationship Between LCM, HCF, and the Numbers:**
- We know the relationship between the two numbers (let's call them \( a \) and \( b \)):
\[ \text{LCM} \times \text{HCF} = a \times b \]
- Given that one number \( a = 125 \):
\[ 800 \times 50 = 125 \times b \]

6. **Solve for the Second Number:**
- Calculate the left side:
\[ 800 \times 50 = 40000 \]
- Now, set up the equation:
\[ 40000 = 125 \times b \]
- To find \( b \), divide both sides by 125:
\[ b = \frac{40000}{125} = 320 \]

7. **Conclusion:**
- The second number is \( 320 \).

### Final Answer:
The second number is **320**.