Average per paper shift: An examinee averages 64 per paper. If he had scored 18 more in Mathematics and 4 more in English, his average would be 66. How many papers were there?

Introduction / Context:
Average increases caused by a known total increment distribute over the number of papers. The increment per paper equals (increase in total marks) / (number of papers).

Given Data / Assumptions:

• Original average = 64
• New average (if extra marks added) = 66
• Extra marks: 18 (Math) + 4 (English) = 22

Concept / Approach:
If n is the number of papers, then adding 22 to the total raises the average by 22/n. This must equal 2 (from 64 to 66), allowing a direct solve for n.

Step-by-Step Solution:

Verification / Alternative check:
Original total = 64n. After adding 22, total becomes 64n + 22. New average = (64n + 22)/n = 64 + 22/n = 66 ⇒ n = 11, consistent.

Why Other Options Are Wrong:

• 9, 13, 15, 10: do not satisfy the condition 22/n = 2.

Common Pitfalls:
Confusing the number of affected papers with total papers; the average shift is spread over all papers, not just the two affected subjects.

Final Answer:
11