A student's marks was wrongly entered as 83 instead of 63. Due to this mistake, the average marks for the class got increased by 1/2. Number of students in the class is equal to :

Question

Accepted Answer

To determine why Option 2 is the correct answer, let's analyze the situation step by step.

1. **Understanding the Problem:**
   - A student's marks were incorrectly recorded as 83 instead of the actual 63.
   - This error caused the average marks of the class to increase by 1/2.

2. **Mathematical Representation:**
   - Let the number of students in the class be $ n $.
   - The incorrect total marks of the class would be the actual total plus the error, which is $ 83 - 63 = 20 $.
   - The increase in average due to this error is $ \frac{1}{2} $.

3. **Equation Setup:**
   - The increase in total marks due to the error is 20.
   - The increase in average marks is given by the formula:
     $$
     \frac{20}{n} = \frac{1}{2}
     $$
   - Solving for $ n $:
     $$
     20 = \frac{1}{2} \times n
     $$
     $$
     n = 40
     $$

4. **Conclusion:**
   - Therefore, the number of students in the class is 40, which corresponds to Option 2.

5. **Explanation of Incorrect Options:**
   - **Option 1 (45):** If there were 45 students, the increase in average would be $ \frac{20}{45} $, which is less than $ \frac{1}{2} $.
   - **Option 3 (35):** If there were 35 students, the increase in average would be $ \frac{20}{35} $, which is more than $ \frac{1}{2} $.
   - **Option 4 (30):** If there were 30 students, the increase in average would be $ \frac{20}{30} $, which is more than $ \frac{1}{2} $.

By following the logical steps and calculations, we confirm that Option 2 is indeed the correct answer, as it satisfies the condition given in the problem.