While tabulation of marks scored in an examination by the students of a class, by mistake the marks scored by one student got recorded as 93 in place of 63, and thereby the average marks increased by 0.5. What was the number of students in the class?

Options

A. 20
B. 30
C. 15
D. 60

Answer

To solve the problem step by step, we can follow these calculations:

1. **Identify the incorrect and correct marks**:
- The marks recorded by mistake: 93
- The actual marks: 63

2. **Calculate the difference in marks**:
- Difference = Recorded marks - Actual marks = 93 - 63 = 30

3. **Understand the impact on average**:
- The average marks increased by 0.5 due to this error.

4. **Let the number of students in the class be \( n \)**.
- The increase in total marks due to the error is 30, and this increase leads to an increase in average marks by 0.5.

5. **Set up the equation for the average**:
- The increase in average marks can be expressed as:
\[ \text{Increase in total marks} = \text{Number of students} \times \text{Increase in average} \]
- This translates to:
\[ 30 = n \times 0.5 \]

6. **Solve for \( n \)**:
- Rearranging the equation gives:
\[ n = \frac{30}{0.5} \]
- Simplifying this:
\[ n = 30 \times 2 = 60 \]

7. **Conclusion**:
- The number of students in the class is 60.