In a competitive test, the minimum passing percentage for girls and boys is 35% and 40% respectively of the same maximum marks. A boy scores 483 marks and fails by 117 marks. What is the minimum passing marks required for a girl in this test?

Introduction / Context:
This percentage question involves pass marks based on different minimum percentages for boys and girls. Such problems check whether you can move between actual marks, percentages and total maximum marks in exams.

Given Data / Assumptions:

• Minimum passing percentage for boys = 40%.• Minimum passing percentage for girls = 35%.• A boy scores 483 marks and fails by 117 marks.• Total maximum marks are the same for boys and girls.• We must find the minimum passing marks for girls.

Concept / Approach:
If a student fails by a certain number of marks, that amount is the difference between the required pass marks and the actual marks obtained. Once we know the pass marks for boys as a percentage of the total, we can find the total maximum marks. Then we use the girls passing percentage to find their pass marks.

Step-by-Step Solution:
Step 1: For the boy, required pass marks = 483 + 117 = 600.Step 2: These 600 marks represent 40% of the total maximum marks.Step 3: Let total maximum marks be M. Then 40% of M = 600.Step 4: So 0.40 * M = 600, hence M = 600 / 0.40 = 1500.Step 5: Girls need 35% of the same total marks to pass.Step 6: Required marks for girls = 0.35 * 1500 = 525.

Verification / Alternative check:
Check proportionality. If 40% of 1500 is 600, then 35% is slightly less than 600. Calculating 10% of 1500 is 150, so 30% is 450, and 5% is 75. Adding 450 and 75 gives 525, which confirms the value.

Why Other Options Are Wrong:
625 is greater than the passing marks for boys and would correspond to more than 40%. 425 and 325 correspond to much lower percentages of 1500 and do not match 35%.

Common Pitfalls:
A common error is to apply the 35% directly on the boy marks instead of on the total maximum marks. Another mistake is forgetting to first add the failure margin to get the boy pass marks.

Final Answer:
The minimum passing marks for girls are 525.