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

Introduction / Context:
This question stresses a very important point in percentage comparison: if one quantity is 50% more than another, the reverse comparison is not 50% less. Many exam questions are designed to expose this misconception. Here, the salary of A is given as 50% more than that of B, and we must compute how much less B earns compared to A, expressed as a percentage of A's salary.

Given Data / Assumptions:

• Let the salary of B be B rupees.
• The salary of A is 50% more than B, so salary of A = B * (1 + 50/100) = 1.5B.
• We need to find the percentage by which B is less than A.
• Required percentage is calculated with A's salary as the base value.

Concept / Approach:
To find how much B is less than A in percentage terms, we first compute the absolute difference, which is A − B. Then we divide this difference by A (the reference quantity) and multiply by 100 to get the required percentage. Because the base of comparison is different in the two directions, the percentage more and percentage less are not equal. Converting the relationship into simple algebra avoids confusion and gives a precise answer.

Step-by-Step Solution:
Step 1: Assume salary of B = B rupees. Step 2: Salary of A is 50% more than B, so A = B * 1.5 = 1.5B. Step 3: Difference in salaries = A − B = 1.5B − B = 0.5B. Step 4: Percentage by which B is less than A = (difference / A) * 100. Step 5: Substitute values: percentage = (0.5B / 1.5B) * 100. Step 6: Simplify the fraction 0.5B / 1.5B = 1/3, so percentage = (1/3) * 100% = 33 1/3%.

Verification / Alternative check:
Take a simple numeric example. Let B = Rs 100. Then A = 150% of 100 = Rs 150. The difference is 150 − 100 = Rs 50. To express this as a percentage of A's salary, compute 50 / 150 * 100 = 33.33%, which is 33 1/3%. This again shows that B's salary is 33 1/3% less than A's salary and confirms the algebraic method.

Why Other Options Are Wrong:

• 50% would almost imply that B has zero salary relative to A, which is not correct because B still earns two thirds of A's salary.
• 44% and 46 1/2% are close looking distractors but they do not match the exact fraction 1/3 that emerges from the algebraic calculation.

Common Pitfalls:
The most common mistake is to assume symmetry and say that if A is 50% more than B, then B is 50% less than A. This ignores that the base for percentage calculation changes. Another error arises from using the wrong base in the formula, for example computing (A − B) / B instead of (A − B) / A when the question clearly asks how much less B is than A. To avoid mistakes, always carefully identify which quantity is taken as 100% in the comparison.

Final Answer:
The salary of B is 33 1/3% less than the salary of A.