The salary of Mr. X is 30% more than the salary of Mr. Y. By what percentage is Mr. Y’s salary less than Mr. X’s salary?

Introduction / Context:
This question tests the important concept that percentage increase in one direction does not equal the percentage decrease in the reverse direction. We are told that Mr. X earns 30% more than Mr. Y, and we must find by what percentage Mr. Y earns less than Mr. X. These relative percentage problems are common in salary, price comparison and profit questions, and they require careful use of ratios rather than simple subtraction of percentages.

Given Data / Assumptions:

Let Mr. Y's salary be Y.

Mr. X's salary is 30% more than Y.

Therefore, Mr. X's salary is X = 1.30Y.

We need to find what percent Mr. Y's salary is less than Mr. X's salary.

Concept / Approach:
The percentage by which Y is less than X is computed as (difference between X and Y) divided by X, multiplied by 100. The difference between their salaries is X - Y. Since X = 1.30Y, the difference becomes 0.30Y. The required percentage is (0.30Y / X) * 100. Substituting X = 1.30Y gives (0.30Y / 1.30Y) * 100. The Y cancels, and we get a percentage that is less than 30%, illustrating the asymmetry between increase and decrease percentages.

Step-by-Step Solution:
Let Mr. Y's salary be Y.Mr. X's salary is 30% more, so X = 1.30Y.Difference in salaries = X - Y = 1.30Y - Y = 0.30Y.We need the percentage by which Y is less than X.Required percentage = (difference / X) * 100.So, required percentage = (0.30Y / 1.30Y) * 100.Simplify the ratio: 0.30Y / 1.30Y = 0.30 / 1.30 = 30 / 130.30 / 130 reduces to 3 / 13.Now convert to percentage: (3 / 13) * 100 ≈ 23.08%.This is approximately equal to 23 1/3%.

Verification / Alternative check:
Assume a convenient value for Y, for example Y = 100 units. Then X = 30% more than 100, which is 130. The difference is 30. Now compute what percent 30 is of X (130). The percentage is (30 / 130) * 100 = 23.08%. This again is approximately 23 1/3%. So Mr. Y's salary is about 23 1/3% less than Mr. X's salary. The exact fraction is 3 / 13, which matches this approximate mixed number.

Why Other Options Are Wrong:

24% and 25 1/2% are larger than the true value and come from rounding errors or using the wrong base for comparison.

22 8/9 % is slightly smaller than the true value and does not match the exact ratio 3 / 13.

30% is the percentage increase from Y to X, not the percentage by which Y is less than X. Using 30% here ignores the change of base.

Common Pitfalls:
The most frequent mistake is to answer 30% directly, forgetting that the base has changed from Y to X. Another pitfall is computing (difference / Y) * 100 instead of (difference / X) * 100, which again yields 30%. Some students also mishandle the fraction 30 / 130 when simplifying. Remember that when the question asks “how much less is Y compared to X,” the base must be X, the larger quantity.

Final Answer:
Mr. Y's salary is approximately 23 1/3% less than Mr. X's salary.