A number is increased by 20% and then decreased by 20%. What is the net change?

Appeared in: AIIMS Delhi NO- 2019

Explanation

When a value is first increased and then decreased by the same percentage, the result is always a net decrease.
This occurs because the percentage decrease is calculated on a larger base number that resulted from the initial increase.
For example, starting with 100, a 20% increase gives 120. A 20% decrease from 120 is 24 (which is larger than the initial increase of 20), resulting in a final value of 96.
The difference between the original value (100) and the final value (96) is 4, which corresponds to a 4% decrease.

Option A: An 8% decrease is a miscalculation. It does not follow the correct formula for successive percentage changes.
Option B: A 4% increase is incorrect. This might result from incorrectly applying the decrease percentage to the original number or a conceptual error. A successive increase and decrease of the same percentage never results in a net increase.
Option D: This is a common misconception. The 20% increase and 20% decrease do not cancel each other out because the base value for the second calculation (the decrease) is different from the original base value.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating successive percentage changes as background academic context rather than a clinical decision trigger.
Understanding percentage change is a fundamental skill required in many nursing calculations, such as titrating medication drips, calculating weight loss or gain in patients, and interpreting changes in lab values.
This problem highlights a common cognitive bias where symmetrical operations are assumed to be reversible or to cancel each other out. In clinical settings, such assumptions can lead to errors in calculation.
What if? If the number was first decreased by 20% and then increased by 20%, the result would be the same: a 4% net decrease. (100 -> 80 -> 96).

How to Approach the Question

Identify that the question asks for the 'net change' after two 'successive' percentage changes (one increase, one decrease).
To simplify the calculation, assume the original number is 100.
Calculate the first change: Increase 100 by 20%. (100 * 0.20 = 20; 100 + 20 = 120).
Apply the second change to the new value: Decrease 120 by 20%. (120 * 0.20 = 24; 120 - 24 = 96).
Compare the final number (96) to the original number (100) to determine the net change. The difference is 4.
Since the final number is less than the original, it is a 4% decrease.

Concept Tested & Keywords

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