The marks of a pupil were wrongly entered as 83 instead of 63, and due to this mistake the average marks of the class increased by 0.5. How many pupils are there in the class?

Introduction / Context:
This problem focuses on how a single incorrect entry can affect the average marks of a class. The marks of one pupil were entered 20 marks higher than the actual marks, resulting in an increase in the class average. We need to determine the class strength from this information. Such questions help students understand the sensitivity of averages to individual data points.

Given Data / Assumptions:
- Correct marks of the pupil should be 63.
- Wrongly entered marks are 83.
- The wrong entry is 20 marks higher than the correct value.
- Due to this mistake, the average marks of the class increased by 0.5 mark.
- Let the number of pupils in the class be n.

Concept / Approach:
The key idea is that a change in one value by a certain amount changes the total sum by the same amount. When average changes, the total change in sum is equal to change in average multiplied by the number of pupils. Here, the total increase in the sum due to the mistake is 20 marks. This must be equal to the increase in average (0.5) multiplied by the number of pupils n, which allows us to solve for n.

Step-by-Step Solution:
Step 1: Extra marks added due to wrong entry = 83 - 63 = 20 marks.Step 2: Let the number of pupils be n.Step 3: Increase in average due to mistake = 0.5 mark.Step 4: Increase in total marks = increase in average * number of pupils = 0.5 * n.Step 5: This increase must equal the extra 20 marks, so 0.5 * n = 20.Step 6: Solve for n: n = 20 / 0.5 = 40.

Verification / Alternative Check:
We can cross check by imagining the correct scenario. If n = 40, then an increase of 0.5 mark in the average means the total marks rise by 40 * 0.5 = 20 marks. This matches exactly the extra marks due to entering 83 instead of 63. Therefore, the class must consist of 40 pupils for this change in average to occur.

Why Other Options Are Wrong:
If there were 45 pupils, then an increase of 0.5 in the average would mean a total increase of 22.5 marks, which does not match the actual extra 20 marks. Similarly, 39 pupils would give total increase of 19.5, and 37 pupils would give total increase of 18.5 marks. Only 40 pupils produce exactly 20 extra marks in total, consistent with the incorrect entry.

Common Pitfalls:
Students sometimes set up the equation incorrectly by dividing 20 by the original average or by using 20 / n = 0.5 instead of 0.5 * n = 20. Another common mistake is to think that the average increases for only one student instead of all students. The correct viewpoint is that the class average is over the entire group, so any change in a single entry affects the sum for all pupils together.

Final Answer:
The class has 40 pupils.