The average of four consecutive odd numbers A,B,C and D respectively is 40. What is the product of B and D ?

Options

A. 1599
B. 1591
C. 1763
D. 1677

Explanation

To solve the problem, we need to find the product of B and D given that the average of four consecutive odd numbers A, B, C, and D is 40.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We know that A, B, C, and D are four consecutive odd numbers. Let's denote the first odd number as \( x \). Therefore, the four consecutive odd numbers can be expressed as:
- A = \( x \)
- B = \( x + 2 \)
- C = \( x + 4 \)
- D = \( x + 6 \)

2. **Calculating the Average**:
The average of these four numbers is given by the formula:
\[ \text{Average} = \frac{A + B + C + D}{4} \]
Substituting the values of A, B, C, and D:
\[ \text{Average} = \frac{x + (x + 2) + (x + 4) + (x + 6)}{4} \]
Simplifying this:
\[ \text{Average} = \frac{4x + 12}{4} = x + 3 \]

3. **Setting Up the Equation**:
We know from the problem statement that the average is 40. Therefore, we can set up the equation:
\[ x + 3 = 40 \]

4. **Solving for x**:
To find \( x \), we subtract 3 from both sides:
\[ x = 40 - 3 = 37 \]

5. **Finding A, B, C, and D**:
Now that we have \( x \), we can find the values of A, B, C, and D:
- A = \( x = 37 \)
- B = \( x + 2 = 37 + 2 = 39 \)
- C = \( x + 4 = 37 + 4 = 41 \)
- D = \( x + 6 = 37 + 6 = 43 \)

6. **Calculating the Product of B and D**:
Now we need to find the product of B and D:
\[ B \times D = 39 \times 43 \]

7. **Performing the Multiplication**:
To calculate \( 39 \times 43 \):
\[ 39 \times 43 = 1677 \]

### Final Answer:
The product of B and D is \( 1677 \).