If the salary of person A is 40 percent less than the salary of person B, then by what percentage is the salary of B greater than the salary of A?

Introduction / Context:
This problem explores forward and reverse percentage changes, a very important concept for salary comparisons, price changes, and profit and loss questions. It is easy to say that one value is 40 percent less than another, but the reverse comparison (how much greater the larger value is than the smaller) does not use the same percentage.

Given Data / Assumptions:
- Let the salary of B be some convenient base value, say 100 units.
- A has 40 percent less salary than B.
- Therefore, salary of A is 60 percent of salary of B.
- We need the percentage by which salary of B is greater than salary of A.

Concept / Approach:
When one quantity is a certain percent less than another, the reverse comparison uses a different percentage because the base changes. We treat B as 100 units, compute A as 60 units, and then ask what percentage 40 units represents when compared to the smaller base of 60 units. The ratio of the difference to the smaller value gives the required percentage.

Step-by-Step Solution:
Step 1: Assume salary of B = 100 units.Step 2: A has 40 percent less than B, so salary of A = 100 - 40 = 60 units.Step 3: The difference between B and A is 100 - 60 = 40 units.Step 4: We need how much greater 100 is compared to 60, expressed as a percentage of 60.Step 5: Required percentage = (Difference / Salary of A) * 100 = (40 / 60) * 100.Step 6: Simplify 40 / 60 = 2 / 3, so percentage = (2 / 3) * 100 = 66 2/3 percent.

Verification / Alternative check:
Another way is to use algebra. Let salary of A be x and salary of B be y. Given that x = 0.6 * y. Then y = x / 0.6. The increase from x to y is y - x = x / 0.6 - x = (x - 0.6 * x) / 0.6 = 0.4 * x / 0.6 = (2 / 3) * x. Percentage increase = (Increase / x) * 100 = (2 / 3) * 100 = 66 2/3 percent, confirming the earlier result.

Why Other Options Are Wrong:
- 33 1/3 percent and 33 2/3 percent are based on confusing the percentage of reduction with the reverse comparison.
- 66 1/3 percent is close but numerically incorrect; the exact value is 66 2/3 percent.

Common Pitfalls:
A very common error is to think that if A is 40 percent less than B, then B must be 40 percent more than A. This is not correct because the base values are different in each comparison. Another mistake is not choosing a convenient base value like 100 units, which makes the arithmetic clearer. Always rebase the percentage when reversing the direction of comparison.

Final Answer:
The salary of B is 66 2/3 percent more than the salary of A.