The difference between two numbers is 5 and their sum is 65. What will be their product

Options

A. (a) 325
B. (b) 650
C. (c) 755
D. (d) 1050

Answer

To solve the problem, we need to find two numbers based on the given conditions: their difference is 5 and their sum is 65. We will denote the two numbers as \( x \) and \( y \).

### Step-by-Step Solution:

1. **Set Up the Equations**:
- From the problem, we have two equations:
\[ x - y = 5 \quad \text{(1)} \]
\[ x + y = 65 \quad \text{(2)} \]

2. **Add the Two Equations**:
- To eliminate \( y \), we can add equations (1) and (2):
\[ (x - y) + (x + y) = 5 + 65 \]
\[ 2x = 70 \]

3. **Solve for \( x \)**:
- Divide both sides by 2:
\[ x = \frac{70}{2} = 35 \]

4. **Substitute \( x \) Back to Find \( y \)**:
- Now, substitute \( x = 35 \) into equation (2):
\[ 35 + y = 65 \]
- Solve for \( y \):
\[ y = 65 - 35 = 30 \]

5. **Calculate the Product**:
- Now that we have both numbers, \( x = 35 \) and \( y = 30 \), we can find their product:
\[ \text{Product} = x \times y = 35 \times 30 \]
- Calculate the product:
\[ 35 \times 30 = 1050 \]

### Final Answer:
The product of the two numbers is \( 1050 \).