In an examination with a maximum of 500 marks, candidate P gets 10% less marks than Q. Candidate Q gets 25% more marks than R and R gets 20% less marks than S. If P scores 360 marks, then what percentage of the maximum marks does S obtain?

Introduction / Context:
This question connects the marks of four candidates through successive percentage increases and decreases. It tests your ability to express each person’s marks in terms of a reference candidate and then convert the final result into a percentage of maximum marks.

Given Data / Assumptions:

• Maximum marks in the exam = 500.• P gets 10% less than Q.• Q gets 25% more than R.• R gets 20% less than S.• P scores 360 marks.• We must find S percentage of 500 marks.

Concept / Approach:
We express every candidate’s marks as a multiple of S marks. Decreases and increases are converted to multiplicative factors. Finally we equate P expression to the given 360 marks and solve for S. Then we convert S marks into a percentage of the maximum 500 marks.

Step-by-Step Solution:
Step 1: Let S marks be x.Step 2: R gets 20% less than S, so R = 0.80x.Step 3: Q gets 25% more than R, so Q = 1.25 * 0.80x = 1.00x.Step 4: P gets 10% less than Q, so P = 0.90 * Q = 0.90x.Step 5: Given P = 360 marks, so 0.90x = 360.Step 6: Solve for x: x = 360 / 0.90 = 400.Step 7: Thus S scored 400 marks out of a maximum of 500.Step 8: Percentage obtained by S = (400 / 500) * 100 = 80%.

Verification / Alternative check:
Check backward: S = 400, R is 20% less so R = 320, Q is 25% more than R so Q = 400, and P is 10% less than Q so P = 360. All conditions match the values, confirming the result.

Why Other Options Are Wrong:
Values 77, 74 and 83% do not give P = 360 when you propagate increases and decreases as per the given relationships. They arise from misinterpreting percentages or using addition instead of multiplication.

Common Pitfalls:
Students sometimes treat a 20% decrease as subtracting 20 marks rather than 20% of the current marks. Another mistake is to apply the percentages in the wrong order or to the wrong candidate.

Final Answer:
S secures 80% of the maximum marks.