A’s salary is 40% more than B’s salary. By what percentage (%) is B’s salary less than A’s salary?

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Points to Remember:

  • This is a mathematical percentage problem.
  • We need to calculate the percentage difference between A’s and B’s salaries.
  • The approach is purely factual and analytical, requiring mathematical calculations.

Introduction:

This question involves a comparison of salaries between two individuals, A and B. We are given that A’s salary is 40% more than B’s salary. The task is to determine the percentage by which B’s salary is less than A’s salary. This requires understanding percentage calculations and applying them to the given information. This is a common type of problem encountered in basic mathematics and percentage applications in various fields like finance and economics.

Body:

Understanding the Problem:

Let’s assume B’s salary is represented by ‘x’. Since A’s salary is 40% more than B’s, A’s salary is x + 0.40x = 1.40x.

Calculating the Percentage Difference:

To find the percentage by which B’s salary is less than A’s salary, we need to calculate the difference between A’s and B’s salaries and express this difference as a percentage of A’s salary.

The difference between A’s and B’s salary is: 1.40x – x = 0.40x

To express this difference as a percentage of A’s salary,

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we divide the difference by A’s salary and multiply by 100:

(0.40x / 1.40x) * 100 = (0.40 / 1.40) * 100 ≈ 28.57%

Therefore, B’s salary is approximately 28.57% less than A’s salary.

Alternative Approach (using a hypothetical example):

Let’s say B’s salary is $100. A’s salary is 40% more, meaning A earns $100 + ($100 * 0.40) = $140.

The difference is $140 – $100 = $40.

The percentage difference relative to A’s salary is ($40 / $140) * 100 ≈ 28.57%. This confirms our earlier calculation.

Conclusion:

In summary, while A’s salary is 40% more than B’s salary, B’s salary is approximately 28.57% less than A’s salary. This difference arises because the base for calculating the percentage difference is different in each case (B’s salary in the first instance and A’s salary in the second). This highlights the importance of clearly defining the base when working with percentages. Understanding percentage calculations is crucial for accurate financial analysis and decision-making in various contexts. This problem emphasizes the need for precise mathematical reasoning and careful interpretation of percentage changes. A clear understanding of percentage calculations promotes financial literacy and responsible financial management.

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