The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is the net change in his salary?

Appeared in: DHS Staff Nurse - 2018 (Shift-2nd)

Explanation

When a value is first increased and then decreased by the same percentage (x%), the net result is always a decrease because the percentage decrease is calculated on a larger base value.
Assuming an initial salary of 100, a 30% increase results in a new salary of 130.
A subsequent 30% decrease is calculated on this new salary of 130, which amounts to a reduction of 39 (0.30 × 130).
The final salary is 130 - 39 = 91.
Comparing the final salary (91) to the original (100), there is a net decrease of 9, which is a 9% decrease.
A shortcut formula for this specific scenario (increase by x%, then decrease by x%) is a net loss of (x²/100)%, which equals (30²/100)% = 9%.

Option A: This is incorrect. The final salary is 91% of the original salary, not a 91% increase. A 91% increase would result in a final salary of 191.
Option B: This is incorrect. The 30% decrease is applied to the higher value after the increase (130), making the reduction amount (39) larger than the initial gain amount (30). Therefore, the net change is not zero.
Option D: This is a common misconception. A percentage increase and a subsequent percentage decrease of the same magnitude do not cancel each other out because the base for each calculation is different.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating net percentage change after successive increases and decreases as background academic context rather than a clinical decision trigger.
This is a quantitative aptitude question, not a clinical one. However, understanding percentage change is a crucial life skill.
This concept is fundamental for financial literacy, helping in understanding salary changes, investments, loan interest, and discounts.
What if? If the salary was first decreased by 30% and then increased by 30%, the result would be the same. A 30% decrease from 100 gives 70. A 30% increase on 70 is 21 (0.30 * 70). The final salary would be 70 + 21 = 91, which is still a 9% decrease.

How to Approach the Question

Identify that the question involves two successive percentage changes on an initial value.
To simplify calculations, assume the initial value is 100, as percentages are based on 100.
First, calculate the result of the initial percentage change (a 30% increase on 100).
Next, apply the second percentage change (a 30% decrease) to the new value obtained in the previous step, not the original one.
Compare the final value to the initial value (100) to find the net difference and express it as a percentage.
Alternatively, recognize the pattern of an x% increase followed by an x% decrease and use the direct formula for net percentage loss: (x²/100)%.

Concept Tested & Keywords

Concept Tested: Calculating net percentage change after successive increases and decreases.
Stem keywords: salary, increased by 30%, reduced by 30%, net change
Lead-in keywords: What is

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