The average of four consecutive numbers. A,B,C and D is 49.5 . What is the product of B and D ?

Options

A. 2499
B. 2352
C. 2450
D. 2550

Explanation

To solve the problem step by step, we will determine the four consecutive numbers based on the given average and then find the product of B and D.

### Step 1: Understand the Problem
We are given that the average of four consecutive numbers A, B, C, and D is 49.5.

### Step 2: Define the Consecutive Numbers
Let’s denote the four consecutive numbers as:
- A = X
- B = X + 1
- C = X + 2
- D = X + 3

### Step 3: Set Up the Average Equation
The average of these four numbers can be expressed as:
\[ \text{Average} = \frac{A + B + C + D}{4} = \frac{X + (X + 1) + (X + 2) + (X + 3)}{4} \]
This simplifies to:
\[ \text{Average} = \frac{4X + 6}{4} \]

### Step 4: Set the Average Equal to 49.5
Since we know the average is 49.5, we can set up the equation:
\[ \frac{4X + 6}{4} = 49.5 \]

### Step 5: Multiply Both Sides by 4
To eliminate the fraction, multiply both sides by 4:
\[ 4X + 6 = 198 \]

### Step 6: Solve for X
Now, subtract 6 from both sides:
\[ 4X = 198 - 6 \]
\[ 4X = 192 \]
Now, divide by 4:
\[ X = 48 \]

### Step 7: Identify the Values of B and D
Now that we have X, we can find the values of B and D:
- B = X + 1 = 48 + 1 = 49
- D = X + 3 = 48 + 3 = 51

### Step 8: Calculate the Product of B and D
Now, we need to find the product of B and D:
\[ B \times D = 49 \times 51 \]

### Step 9: Perform the Multiplication
Calculating the product:
\[ 49 \times 51 = 2499 \]

### Final Answer
The product of B and D is **2499**.

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