In an examination with maximum marks of 500, K gets 10% less marks than L, L gets 25% more marks than M, and M gets 20% less marks than N. If K scores 360 marks, what percentage of the maximum marks does N obtain?

Introduction / Context:
This question involves a chain of percentage relations between the marks of four students K, L, M and N in an examination with a known maximum score. We are given that K scores 10% less than L, L scores 25% more than M, and M scores 20% less than N. The score of K is known, and we must ultimately find the percentage of maximum marks obtained by N. This tests the ability to move through multiple percentage relationships systematically.

Given Data / Assumptions:

Maximum marks in the examination are 500.

K gets 10% less than L.

L gets 25% more than M.

M gets 20% less than N.

K's marks are given to be 360.

We must find N's marks as a percentage of 500.

Concept / Approach:
We work backward from the known value. Starting with K = 360, we express each relation in terms of the previous one. If K is 10% less than L, then K = 0.90L. If L is 25% more than M, then L = 1.25M. If M is 20% less than N, then M = 0.80N. Combining these, we can express K directly in terms of N, solve for N, and then compute N's percentage of 500. This chain method keeps the structure clear and avoids confusion.

Step-by-Step Solution:
Let N's marks be N.M gets 20% less than N, so M = 0.80N.L gets 25% more than M, so L = 1.25M = 1.25 * 0.80N = 1.00N.Thus L = N.K gets 10% less than L, so K = 0.90L = 0.90N.Given K = 360, so 0.90N = 360.Therefore N = 360 / 0.90 = 400.N's percentage of the maximum 500 marks is (400 / 500) * 100.Compute: (400 / 500) * 100 = 80%.

Verification / Alternative check:
Check all relationships using N = 400. M = 20% less than N, so M = 0.80 * 400 = 320. L is 25% more than M, so L = 1.25 * 320 = 400. Thus L and N both have 400 marks, consistent with the earlier result. K is 10% less than L, so K = 0.90 * 400 = 360, which matches the given score. This confirms that the chain of calculations is correct and N's marks are 400, corresponding to 80% of 500.

Why Other Options Are Wrong:

87, 78 and 76 percent would correspond to different total marks and would break the relationships among K, L, M and N.

82% of 500 is 410 marks, which does not satisfy the given conditions when propagated back through M, L and K.

Common Pitfalls:
Students often confuse phrases like 10% less than and 10% of, or mistakenly apply increments and decrements in the wrong direction. Another error is trying to work from N downward without anchoring values, which can be messy. Instead, starting from the known score, expressing each relation as a multiplier and solving systematically keeps the work organized. Remember that less than means multiplying by (1 - percentage / 100), while more than means multiplying by (1 + percentage / 100).

Final Answer:
Mr. N obtains 80 percent of the maximum marks in the examination.