In an exam there were 5 Questions, 5% of give all 5 answer ,5% didn't give  any answer , 20% of remaining give 1answer , 25% give 2 answer and 24.5 of total candidate give 4 answer . If 996candidates give 3 and then find the total no. Of candidates in the exam

Let the total number of candidates in the exam be denoted as \( N \).

### Step 1: Break down the information provided

1. **5% gave all 5 answers**: This is \( 0.05N \).
2. **5% didn’t give any answers**: This is also \( 0.05N \).
3. **Of the remaining candidates, 20% gave 1 answer**.
    - Remaining candidates after subtracting the above two groups: \( N - 0.05N - 0.05N = 0.9N \).
    - 20% of these remaining candidates gave 1 answer: \( 0.2 \times 0.9N = 0.18N \).
4. **25% gave 2 answers**: 
    - Again, of the remaining \( 0.9N \), 25% gave 2 answers: \( 0.25 \times 0.9N = 0.225N \).
5. **24.5% of the total candidates gave 4 answers**: This is \( 0.245N \).
6. **996 candidates gave 3 answers**: This is given directly as 996 candidates.

### Step 2: Formulate the equation
The total number of candidates \( N \) is the sum of all these groups:

\[
N = 0.05N + 0.05N + 0.18N + 0.225N + 0.245N + 996
\]

### Step 3: Combine like terms

\[
N = (0.05 + 0.05 + 0.18 + 0.225 + 0.245)N + 996
\]
\[
N = 0.75N + 996
\]

### Step 4: Solve for \( N \)

Rearranging the equation to isolate \( N \):

\[
N - 0.75N = 996
\]
\[
0.25N = 996
\]
\[
N = \frac{996}{0.25} = 3984
\]

### Step 5: Conclusion
The total number of candidates in the exam is \( \boxed{3984} \).

Would you like to see more details, or have any questions?

Here are 5 related questions:
1. How would the solution change if 15% gave all 5 answers instead of 5%?
2. What if 50% of the remaining candidates gave 1 answer?
3. How can this method be applied to surveys with similar categorical breakdowns?
4. What is the proportion of candidates who gave exactly 2 answers?
5. How can we model this scenario using a weighted probability distribution?

**Tip**: In problems involving percentages, always account for the total population to ensure your breakdown covers everyone!

In an exam there were 5 Questions, 5% of give all 5 answer, 5% didn't give any answer, 20% of remaining give 1 answer, 25% give 2 answer and 24.5 of total candidate give 4 answer. If 996 candidates give 3, then find the total number of candidates in the exam.

Learn how to calculate the total number of candidates in an exam where the distribution of answers is given in percentages. This problem uses algebra, percentages, and linear equations to solve for the total number of candidates. Suitable for Grades 8-10.

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