The average of five consecutive odd number is 61. Then the difference between the highest and lowest numbers is

Options

A. 2
B. 5
C. 8
D. Cannot be determined

Answer

To solve the problem, we need to find the difference between the highest and lowest numbers among five consecutive odd numbers, given that their average is 61.

### Step-by-Step Solution:

1. **Understanding the Average**:
The average of five consecutive odd numbers is given as 61. The average can be calculated using the formula:
\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Number of numbers}} \]
Therefore, we can express the sum of the five numbers as:
\[ \text{Sum of numbers} = \text{Average} \times \text{Number of numbers} = 61 \times 5 = 305 \]

2. **Defining the Consecutive Odd Numbers**:
Let the five consecutive odd numbers be represented as:
\[ x, x+2, x+4, x+6, x+8 \]
Here, \(x\) is the smallest odd number among them.

3. **Calculating the Sum**:
The sum of these five numbers can be expressed as:
\[ x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 5x + 20 \]

4. **Setting Up the Equation**:
We know from step 1 that the sum is 305. Therefore, we can set up the equation:
\[ 5x + 20 = 305 \]

5. **Solving for \(x\)**:
To find \(x\), we first subtract 20 from both sides:
\[ 5x = 305 - 20 = 285 \]
Now, divide both sides by 5:
\[ x = \frac{285}{5} = 57 \]

6. **Finding the Five Consecutive Odd Numbers**:
Now that we have \(x\), we can find the five consecutive odd numbers:
\[ 57, 59, 61, 63, 65 \]

7. **Finding the Highest and Lowest Numbers**:
The highest number is 65 and the lowest number is 57.

8. **Calculating the Difference**:
The difference between the highest and lowest numbers is:
\[ 65 - 57 = 8 \]

### Final Answer:
The difference between the highest and lowest numbers is **8**.