A number is increased by 20% and then decreased by 20%. Find the net increase or decrease percentage.

Appeared in: NHM UP Staff Nurse-2023 Shift-2nd

Explanation

When a value is first increased and then decreased by the same percentage (x%), the net result is always a percentage decrease.
To calculate this, you can assume a starting number like 100. A 20% increase makes it 120.
Then, a 20% decrease is calculated on the new value (120), not the original 100. 20% of 120 is 24.
Subtracting this from 120 gives the final number: 120 - 24 = 96.
The change from the original 100 to the final 96 is a decrease of 4, which represents a 4% decrease.
A shortcut formula for this specific scenario is (x²/100)% decrease. For x=20, this is (20*20)/100 = 4% decrease.

Option A: A 0% change is incorrect because the 20% increase and 20% decrease are calculated on different base amounts. The decrease is calculated on a larger number, resulting in a larger absolute change.
Option C: This is conceptually the same as the '0% increase' option. The final value is not the same as the original value because the percentage decrease is applied to a larger base.
Option D: A net increase is impossible. The value of the decrease (20% of 120 = 24) is greater than the value of the increase (20% of 100 = 20), so the final result must be lower than the starting point.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of successive percentage change as background academic context rather than a clinical decision trigger.
This question tests fundamental numeracy, a critical skill for nurses in various tasks like medication dosage calculation, fluid balance monitoring, and interpreting changes in patient metrics.
For example, understanding percentage change is vital when assessing weight loss or gain in a patient (e.g., a 10% weight loss in a month is a significant clinical finding).
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 the core task: calculating the net effect of a percentage increase followed by a percentage decrease.
Recognize that the base for the second percentage change is different from the original base.
Method 1 (Calculation): Assume a simple starting number like 100. First, calculate the increase: 100 * 1.20 = 120.
Next, calculate the decrease on the new number: 120 * 0.80 = 96.
Finally, determine the net percentage change from the original number (100) to the final number (96), which is a 4% decrease.
Method 2 (Shortcut): Recall the formula for successive equal percentage increase and decrease: Net change is a decrease of (x²/100)%. Substitute x=20 to get (400/100) = 4% decrease.

Concept Tested & Keywords

QU4KXtEO7DIYnOHQq0GY7z

Practise the full NHM UP Staff Nurse-2023 Shift-2nd

Attempt every question from this paper in a timed mock, then review the full solution for each one.