Three students A, B and C appear in an examination. A scores 36% fewer marks than B and 16% more marks than C. If B scores 145 marks, how many marks does C score?

Introduction / Context:

This question again focuses on percentage relationships between the marks of three students. It combines a percentage decrease relationship between A and B and a percentage increase relationship between A and C. These kinds of problems help you understand how to move between values when given relative percentage comparisons.

Given Data / Assumptions:

• B scores 145 marks.
• A scores 36% less than B.
• A scores 16% more than C.
• All marks are from the same test and are comparable.

Concept / Approach:

We first compute A's marks using the fact that A scores 36% less than B, so A is 64% of B. Then we use the relation that A is 16% more than C, which means A is 116% of C or 1.16 * C. By equating these two expressions for A, we can solve for C. This process converts the verbal relationships into a solvable equation.

Step-by-Step Solution:

Verification / Alternative check:

Check with C = 80. A is 16% more than C, so A = 80 + 16% of 80 = 80 + 12.8 = 92.8, which matches our value for A. Now B should be such that A is 36% less than B. If B = 145, then 36% of 145 is 52.2, and B − 36% of B = 145 − 52.2 = 92.8. This matches A again, so the relationships are consistent.

Why Other Options Are Wrong:

• 120 and 110: These are larger than 92.8, so A could not be 16% more than C if C were this large.
• 75: If C were 75, then A as 16% more than C would be 87, which does not fit with the computed 92.8.
• 90: Similarly gives A = 90 + 16% of 90 = 104.4, which is too large compared to 92.8.

Common Pitfalls:

A frequent mistake is reversing the direction of the percentage change, for example treating 36% less as 64% more or misreading 16% more than C as C being 16% more than A. Another common error is computing percentages using approximations and rounding too early, which can distort the result. Carefully set up each relationship using the correct base value.

Final Answer:

C scores 80 marks.