यदि 408 एवं 1032 के मo सo (HCF) को 1032p-408xx5` के रूप में व्यक्त कर सकते हो तो p=?

Options

A. 2
B. 3
C. 4
D. 5

Answer

To solve the problem, we need to express the sum of 408 and 1032 in the form of \( 1032p - 408 \times 5 \) and find the value of \( p \).

### Step-by-Step Solution:

1. **Calculate the sum of 408 and 1032:**
\[ 408 + 1032 = 1440 \]

**Hint:** To find the sum, simply add the two numbers together.

2. **Set up the equation:**
We need to express this sum in the form of \( 1032p - 408 \times 5 \). Therefore, we can write:
\[ 1440 = 1032p - 408 \times 5 \]

**Hint:** Write the equation based on the given expression and the sum you calculated.

3. **Calculate \( 408 \times 5 \):**
\[ 408 \times 5 = 2040 \]

**Hint:** Multiply 408 by 5 to simplify the equation.

4. **Substitute \( 2040 \) into the equation:**
\[ 1440 = 1032p - 2040 \]

**Hint:** Replace \( 408 \times 5 \) with its calculated value in the equation.

5. **Rearrange the equation to isolate \( 1032p \):**
\[ 1032p = 1440 + 2040 \]
\[ 1032p = 3480 \]

**Hint:** Move \( 2040 \) to the left side by adding it to 1440.

6. **Solve for \( p \):**
\[ p = \frac{3480}{1032} \]

**Hint:** Divide both sides by 1032 to find the value of \( p \).

7. **Calculate the value of \( p \):**
\[ p = \frac{3480 \div 12}{1032 \div 12} = \frac{290}{86} = \frac{145}{43} = 3.372 \approx 3 \]

**Hint:** Simplify the fraction to find the integer value of \( p \).

### Final Answer:
The value of \( p \) is approximately \( 3 \).