In an examination paper of five questions, `5%` of the candidates answered all of them and `5%` answered none. Of the rest, `25%` candidates answered only one question and 20% answered 4 questions. If 396 candidates answered either 2 questions or 3 questions, the number of candidates that appeared for the examination was

Options

A. 800
B. 1000
C. 850
D. 900

Answer

To solve the problem step by step, let's denote the total number of candidates who appeared for the examination as \( N \).

### Step 1: Determine the percentages of candidates
- 5% of candidates answered all questions: \( 0.05N \)
- 5% of candidates answered none: \( 0.05N \)
- Therefore, the candidates who answered either all or none:
\[ 0.05N + 0.05N = 0.1N \]

### Step 2: Calculate the remaining candidates
- The remaining candidates who answered either 1, 2, 3, or 4 questions:
\[ N - 0.1N = 0.9N \]

### Step 3: Determine the distribution of the remaining candidates
- According to the problem:
- 25% answered only 1 question:
\[ 0.25 \times 0.9N = 0.225N \]
- 20% answered 4 questions:
\[ 0.20 \times 0.9N = 0.18N \]

### Step 4: Calculate the total percentage accounted for
- Adding those who answered 1 question and those who answered 4 questions:
\[ 0.225N + 0.18N = 0.405N \]
- Therefore, the remaining candidates who answered either 2 or 3 questions:
\[ 0.9N - 0.405N = 0.495N \]

### Step 5: Set up the equation for candidates answering 2 or 3 questions
- We know that 396 candidates answered either 2 or 3 questions:
\[ 0.495N = 396 \]

### Step 6: Solve for \( N \)
- To find \( N \), divide both sides by 0.495:
\[ N = \frac{396}{0.495} \]
- Calculating \( N \):
\[ N = 800 \]

### Conclusion
The total number of candidates that appeared for the examination is \( \boxed{800} \).

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