Salary increased by 15% then decreased by 15%. Net change:

Appeared in: UP NHM CHO 7 Sept 2022 (Shift-2)

Explanation

When a quantity is increased by x% and then decreased by x%, there is always a net percentage decrease.
The formula for this net decrease is (x² / 100)%.
Substituting x = 15, the net decrease is (15 * 15) / 100 = 225 / 100 = 2.25%.
Alternatively, using a base of 100: 100 increases to 115. A 15% decrease on 115 is 17.25, leading to a final value of 97.75, which is a 2.25% decrease from 100.

Option B: This option suggests a large increase. A successive increase and decrease by the same percentage never results in a net increase. The value 22.5 is also incorrect, likely due to a calculation error.
Option C: This option incorrectly suggests a net increase. The 15% decrease is calculated on a larger base (the salary after the increase), so the amount of decrease is larger than the amount of the initial increase, resulting in a net loss.
Option D: This option has the correct direction (decrease) but an incorrect magnitude. The value 22.5% is a result of a decimal point error in the calculation (e.g., misinterpreting 225/100).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Successive Percentage Change as background academic context rather than a clinical decision trigger.
This type of calculation is fundamental in finance for understanding compound interest, investment returns, and the effect of discounts on marked-up prices.
It helps in developing critical thinking to avoid common fallacies, such as assuming that a 15% gain followed by a 15% loss returns you to the starting point.
What if? If the salary first decreased by 15% and then increased by 15%, the result would be identical. 100 -> 85. Then, 15% of 85 is 12.75. 85 + 12.75 = 97.75. The net change is still a 2.25% decrease, proving the order does not matter.

How to Approach the Question

Identify the question as a successive percentage change problem where the percentage increase and decrease are the same.
Recall the shortcut formula for this specific scenario: Net Percentage Decrease = (x² / 100)%, where 'x' is the percentage change.
Substitute the given percentage, x = 15, into the formula.
Calculate: (15 * 15) / 100 = 225 / 100 = 2.25.
Conclude that the net change is a 2.25% decrease.
Alternatively, assume a starting value of 100, apply the 15% increase (100 -> 115), then apply the 15% decrease to the new value (115 * 0.85 = 97.75), and calculate the difference from the start (100 - 97.75 = 2.25).

Concept Tested & Keywords

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Practise the full UP NHM CHO 7 Sept 2022 (Shift-2)

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