If A scored 20% more marks than B, by what percentage are the marks of B less than the marks of A?

Introduction / Context:
This question is about the relationship between two quantities when one is a given percentage more than the other. It highlights an important concept that percentage increase and percentage decrease between two values are not symmetric. If A is 20 percent more than B, the percentage by which B is less than A is not 20 percent, but a different value that must be computed carefully.

Given Data / Assumptions:
Marks of B are taken as a base reference value.
A scored 20 percent more marks than B.
We need the percentage by which B is less than A.
We assume marks are positive numbers and percentages are based on standard definitions.

Concept / Approach:
Let the marks of B be 100 units for simplicity. Then a 20 percent increase means A has 120 marks. The percentage by which B is less than A is calculated using A as the base, because the question asks relative to A. So we compute (A - B) / A * 100 percent. With A = 120 and B = 100, the difference is 20. Therefore the required percentage is 20 / 120 * 100, which simplifies to 16.66 percent (approximately). This illustrates that a 20 percent increase from B to A corresponds to about a 16.66 percent decrease when going from A back to B.

Step-by-Step Solution:
Assume marks of B = 100 units. A scored 20 percent more than B, so marks of A = 100 + 20 percent of 100. 20 percent of 100 = 20, so marks of A = 120. Now we find by what percent B is less than A. Difference in marks = A - B = 120 - 100 = 20. Required percentage = (difference / A) * 100 = (20 / 120) * 100. Compute 20 / 120 = 1 / 6, and 1 / 6 * 100 = 16.66 percent (approximately). Therefore, the marks of B are 16.66 percent less than the marks of A.

Verification / Alternative check:
We can choose any convenient number for B, not just 100, and the percentage will be the same. For example, let B = 50. Then A is 20 percent more, so A = 50 + 0.20 * 50 = 60. The difference is 10. Now the percentage by which B is less than A is (10 / 60) * 100 = 16.66 percent. This confirms that the result does not depend on the particular starting value chosen, as the ratio remains constant.

Why Other Options Are Wrong:
20 percent would be correct only if we compared relative to B instead of A, which is not what the question asks. 33.33 percent corresponds to a situation where one value is half of the other, which is not the case here. The value 14.28 percent corresponds roughly to 1 / 7 and does not fit the actual ratio 100 to 120. Only 16.66 percent correctly represents how much smaller B is compared to A when A is 20 percent more than B.

Common Pitfalls:
The most common mistake is to assume that if A is 20 percent more than B, then B is automatically 20 percent less than A. This is incorrect because the bases for the two percentages are different. Another error is to subtract 20 from 100 and say the answer is 80 percent, completely misinterpreting the question. Always identify clearly which value is being taken as the base for the percentage comparison and set up the ratio accordingly.

Final Answer:
The marks of B are approximately 16.66 percent less than the marks of A.