In a Mathematics examination the numbers scored by 5 candidates are 5 successive odd integers . If their total marks is 185, the highest score is

Options

A. 39
B. 43
C. 41
D. 37

Answer

To solve the problem, we need to find the highest score among 5 candidates who scored 5 successive odd integers that sum up to 185.

### Step-by-Step Solution:

1. **Define the Variables**:
Let the smallest odd integer be represented as \( x \). The five successive odd integers can then be expressed as:
- First integer: \( x \)
- Second integer: \( x + 2 \)
- Third integer: \( x + 4 \)
- Fourth integer: \( x + 6 \)
- Fifth integer: \( x + 8 \)

2. **Set Up the Equation**:
The total of these five integers is given as 185. Therefore, we can set up the equation:
\[ x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 185 \]

3. **Combine Like Terms**:
Simplifying the left side of the equation:
\[ x + x + 2 + x + 4 + x + 6 + x + 8 = 185 \]
This simplifies to:
\[ 5x + 20 = 185 \]

4. **Solve for \( x \)**:
To isolate \( x \), subtract 20 from both sides:
\[ 5x = 185 - 20 \]
\[ 5x = 165 \]
Now, divide both sides by 5:
\[ x = \frac{165}{5} = 33 \]

5. **Find the Highest Score**:
The highest score among the five integers is:
\[ x + 8 = 33 + 8 = 41 \]

### Final Answer:
The highest score is **41**.

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