By what percentage must a salary be decreased so that the decrease exactly cancels out a previous 20% increase in that salary?

Introduction / Context:
This question is a classic example of successive percentage change, where an initial increase is followed by a decrease and we want to return to the original value. It tests whether learners understand that a 20% increase and a 20% decrease do not cancel each other out. Instead, the second percentage must be carefully calculated so that the combined effect of both changes brings the value back to its starting point. This concept is important in salary revisions, pricing, and discount related aptitude questions.

Given Data / Assumptions:

• The salary is first increased by 20%.
• We want to apply a decrease afterwards so that the final salary becomes equal to the original salary.
• The required decrease is to be expressed as a percentage of the increased salary.
• No actual salary amount is given, so we are free to assume a convenient starting value, such as 100 units.

Concept / Approach:
The natural method is to assume an initial salary and apply the percentage changes step by step using multiplication factors. If the original salary is taken as 100 units, then a 20% increase turns it into 120 units. After this increase, the new salary is 120, and we must find a percentage decrease x% such that applying it to 120 brings the salary back to 100. This leads to a simple equation in one variable. The core concept is understanding that percentage changes are multiplicative rather than additive, especially when they occur successively.

Step-by-Step Solution:
Step 1: Assume the original salary is 100 units.Step 2: A 20% increase means the new salary is 100 + 20% of 100 = 100 + 20 = 120 units.Step 3: Let the required percentage decrease be x% applied to 120 to return to 100.Step 4: After the decrease, the new value is 120 * (1 - x/100).Step 5: Set this equal to the original salary: 120 * (1 - x/100) = 100.Step 6: Divide both sides by 120 to get 1 - x/100 = 100 / 120 = 5/6.Step 7: Rearrange to get x/100 = 1 - 5/6 = 1/6.Step 8: Therefore x = 100 * (1/6) = 16 2/3 percent.

Verification / Alternative check:
We can verify by applying the found decrease. Start with 100 units, increase by 20% to get 120 units. Now decrease 120 by 16 2/3 percent. The decrease amount is (16 2/3 / 100) * 120 = (1/6) * 120 = 20 units. Subtracting this from 120 gives 120 - 20 = 100 units, which is exactly the original salary. This confirms that the calculated percentage decrease of 16 2/3% is correct and precisely cancels the initial 20% increase.

Why Other Options Are Wrong:
Option (15 + 2/3)% is less than the required figure, so after decreasing by that amount, the salary would still be above 100. Option (14 + 1/3)% is even smaller and would leave the salary higher than its starting value. Option (13 + 4/5)% represents a still smaller decrease and is clearly insufficient. Option 20% might look attractive because it matches the initial increase, but applying 20% decrease to 120 leads to 96, not 100, so it does not cancel the increase. Only 16 2/3% restores the original value exactly.

Common Pitfalls:
The most frequent mistake is to assume that a 20% increase can be cancelled by a 20% decrease, which ignores the fact that the second percentage is applied to a changed base. Another common error is treating the percentages additively rather than multiplicatively, for example, writing 20 - x = 0 or 20 + x = 0 without using the correct equation. Some learners also skip the algebra and attempt mental approximations, increasing the chance of error. Always write down the multiplicative factors and set up the equation carefully.

Final Answer:
The salary must be decreased by 16 2/3% to exactly cancel out the 20% increase.