In a school, 75 pupils appeared for an examination and 80% of them passed.\nAnother school sent 10 more pupils than the first school, and 5 fewer pupils passed than in the first school.\nWhat was the pass percentage in the second school?

Introduction / Context:
This problem compares examination performance in two schools using numbers of pupils and pass percentages. The first school's data is given directly, and the second school's information is given relative to the first. You must determine the pass percentage for the second school. This tests your ability to convert between absolute numbers and percentages and to reason across two related scenarios.

Given Data / Assumptions:

• First school: 75 pupils appeared, and 80% passed.
• Second school: number of pupils who appeared is 10 more than the first school.
• Number of pupils who passed in the second school is 5 less than in the first school.
• We must find the pass percentage in the second school.
• All pupils either pass or fail; there are no other categories.

Concept / Approach:
First, compute the number of pupils who passed in the first school using 80% of 75. Then use the given relations to find both the number of pupils who appeared and the number who passed in the second school. Finally, compute the pass percentage in the second school as (passed / appeared) * 100. Converting everything into actual counts before finding the percentage keeps the reasoning clear.

Step-by-Step Solution:
Step 1: First school: pupils appeared = 75. Step 2: Pass count in first school = 80% of 75. Step 3: Compute 80% of 75: (80 / 100) * 75 = 0.8 * 75 = 60. So 60 pupils passed in the first school. Step 4: Second school: pupils appeared = 10 more than 75 = 75 + 10 = 85. Step 5: Pupils passed in second school = 5 fewer than in first school = 60 − 5 = 55. Step 6: Pass percentage in second school = (55 / 85) * 100. Step 7: Simplify the fraction 55 / 85 = 11 / 17. Step 8: Compute (11 / 17) * 100 ≈ 64.705..., which is usually written as 64.7% (approx).

Verification / Alternative check:
We can check the reasonableness: in the first school, 60 out of 75 passed, giving 80%. In the second school, more students appeared (85), but fewer passed (55), so the pass percentage must be lower than 80%. Our result of about 64.7% is indeed less than 80%, and when reversed, 64.7% of 85 is approximately 55, consistent with the given data.

Why Other Options Are Wrong:
75%: Would correspond to about 63.75 passing out of 85, which does not match the actual 55 passes.

84% and 72%: Both are higher than 64.7%, and using them would produce pass counts significantly different from 55 when multiplied by 85.

68%: Closer but still higher than the correct value; 68% of 85 is 57.8, not 55.

Common Pitfalls:
Some students mistakenly take 80% of 85 or misread the relationship about 5 fewer passes. Others compute the pass percentage by subtracting 5 from 80 directly, which incorrectly mixes absolute counts and percentages. Always convert percentages to actual student counts in each school and then recompute the percentage for the second school from those counts.

Final Answer:
The pass percentage in the second school is approximately 64.7%.