In a class, one pupil's marks were wrongly entered as 83 instead of 63. Because of this single error, the average marks for the whole class increased by 0.5 marks. How many pupils are there in the class?

Introduction / Context:
This question involves a classic average error scenario. One student's marks were recorded incorrectly, and this mistake caused the class average to change. By comparing the original correct total and the incorrect total implied by the faulty entry, we can find the number of pupils in the class using a simple algebraic equation.

Given Data / Assumptions:

• One pupil's correct marks = 63.
• Marks were wrongly entered as 83.
• Difference between incorrect and correct marks = 83 - 63 = 20.
• This error increased the average marks of the class by 0.5 marks.
• Let the number of pupils in the class be n.

Concept / Approach:
If the average increases by 0.5 marks for n pupils, then the total increase in marks must be: increase in total marks = n * 0.5. But we also know that the incorrect entry added 20 extra marks to the total. By equating these two expressions for the increase in total marks, we can solve for n.

Step-by-Step Solution:
Step 1: Extra marks added due to error = 83 - 63 = 20. Step 2: Because of this, the average for the whole class increased by 0.5 marks. Step 3: Let the number of pupils be n. Step 4: Increase in total marks due to rise in average = n * 0.5. Step 5: This increase must equal the extra 20 marks from the wrong entry. Therefore, n * 0.5 = 20. Step 6: So n = 20 / 0.5 = 20 * 2 = 40.
Verification / Alternative check:
If n = 40, then an increase of 0.5 in average means total marks increased by 40 * 0.5 = 20, which matches the extra marks due to the wrong entry. Thus, the calculation is consistent and confirms that n = 40.
Why Other Options Are Wrong:
If n were 45, the increase in total would be 45 * 0.5 = 22.5, which does not match the extra 20 marks. Similarly, for n = 39, the increase would be 19.5; for n = 37, it would be 18.5; for n = 50, it would be 25. None of these equal 20.
Common Pitfalls:
A frequent mistake is to divide 20 by 0.5 incorrectly (for example, getting 10 instead of 40). Another error is to forget to connect increase in average across the entire class with the total increase in marks.
Final Answer:
The number of pupils in the class is 40.