Three students A, B and C appear in an examination. A scores 18% more marks than B and 12% fewer marks than C. If B scores 220 marks, how many marks does C score in the same exam?

Introduction / Context:

This question combines percentage increase and decrease in the context of examination marks. You are given relational information about how much more A scores than B and how much less A scores than C. Such problems are very common in aptitude tests under the percentage or ratio category and help develop flexibility in handling linked percentage relationships.

Given Data / Assumptions:

• B scores 220 marks.
• A scores 18% more than B.
• A scores 12% less than C.
• All marks are from the same examination and are comparable.

Concept / Approach:

The approach is to first express A's marks in terms of B using the 18% increase. Then, use the information that A's marks are 12% less than C to link A and C. If A is 12% less than C, then A is 88% of C or 0.88 * C. Setting the two expressions for A equal allows us to solve for C.

Step-by-Step Solution:

Verification / Alternative check:

We can verify this value of C. If C = 295, then 12% of 295 is 0.12 * 295 = 35.4. Subtracting this from 295 gives 295 − 35.4 = 259.6, which matches A's marks. Also, check A relative to B: B has 220, and A has 259.6, which is 39.6 more. The percentage increase is 39.6 / 220 * 100 = 18%, confirming the consistency.

Why Other Options Are Wrong:

• 245: If C were 245, then 12% less than 245 would be 245 − 29.4 = 215.6, which does not match A's marks.
• 230: Twelve percent less than 230 is 202.4, again not compatible with an 18% increase from B's 220 marks.
• 224: Similarly, 12% less than 224 is 197.12, which is too low and inconsistent with the data.
• 260: If C were 260, 12% less would be 228.8, which does not produce the correct relationship to B.

Common Pitfalls:

A frequent mistake is to treat 18% more and 12% less with respect to the wrong base, such as applying both directly on B or C. Another typical error is to subtract percentages directly instead of forming algebraic equations. Always express each relationship carefully in equation form and keep track of which percent relates to which student.

Final Answer:

C scores 295 marks.