The salary of A is 50 percent more than the salary of B. By what percentage is B's salary less than A's salary?

Introduction / Context:
This is a classic percentage comparison question where one quantity is more than another by a certain percent and we are asked to reverse the comparison. Many students wrongly assume the percentages will be the same in both directions, which is not true in percentage arithmetic.

Given Data / Assumptions:

• A's salary is 50 percent more than B's salary.
• We need the percentage by which B's salary is less than A's salary.
• Salaries are positive numbers and we use simple percentage definitions.

Concept / Approach:
When A is 50 percent more than B, it means A = B + 0.5 * B = 1.5 * B. To find how much B is less than A, we compare the difference (A - B) with A, not with B. This is where many candidates go wrong, because the base for the percentage changes when we reverse the comparison.

Step-by-Step Solution:
Assume B's salary = 100 units for ease of calculation.Then A's salary = 100 + 50 = 150 units.Difference between A and B = 150 - 100 = 50 units.Required percentage = (difference / A) * 100.So percentage by which B is less than A = (50 / 150) * 100 = 33.33 percent (approximately).

Verification / Alternative check:
We can scale salaries to any convenient real values. For example, if B earns Rs. 20,000, then A earns 1.5 * 20,000 = Rs. 30,000. The difference is Rs. 10,000. The percentage by which B is less than A is 10,000 / 30,000 * 100 = 33.33 percent, which matches the earlier calculation.

Why Other Options Are Wrong:
Values like 24.5 percent, 29.5 percent and 31.3 percent come from using wrong bases or approximate mental arithmetic. None of these percentages correctly represent the ratio of the difference to A's salary. Only 33.3 percent is consistent with the exact ratio 1/3.

Common Pitfalls:
A very common error is to say that if A is 50 percent more than B, then B is 50 percent less than A, which is incorrect because percentage change always depends on the reference quantity. Another mistake is to divide the difference by B instead of A while answering the reversed question.

Final Answer:
B's salary is approximately 33.3 percent less than A's salary.