What is the total discount applied when 3 successive discounts of 25 percent, 15 percent and 12.5 percent are applicable?

Appeared in: DSSSB -28 August 2019 (Shift-2)

Explanation

Successive discounts are applied sequentially on the reduced price, not on the original price.
The correct method is to calculate the remaining price factor after each discount and multiply them together.
The remaining factors are (1 - 0.25) = 0.75, (1 - 0.15) = 0.85, and (1 - 0.125) = 0.875.
The final price factor is 0.75 × 0.85 × 0.875 = 0.5578125.
The total discount is calculated as (1 - final price factor) × 100, which is (1 - 0.5578125) × 100 = 44.21875%.
Rounding to two decimal places gives 44.22%.

Option A: This value is incorrect and likely results from a calculation error, such as miscalculating one of the intermediate discount steps or an arithmetic mistake in multiplication.
Option C: This value is incorrect. It may arise from incorrectly combining the percentages, for example, by rounding intermediate steps prematurely, which leads to an inaccurate final result.
Option D: This value is incorrect. A common mistake that could lead to a value in this range is incorrectly applying the formula or making an error in the multiplication of the decimal factors.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of successive percentage discounts as background academic context rather than a clinical decision trigger.
While a math problem, the principle of successive percentage change is vital in healthcare. For example, when preparing serial dilutions of a medication, the concentration is reduced stepwise, following the same multiplicative principle.
This concept also applies to understanding the decay of radioactive isotopes used in diagnostics or therapy, where the remaining activity decreases by a certain percentage over each half-life.
In hospital administration, this calculation is used for financial planning, such as applying multiple discounts on bulk purchases of medical equipment or supplies.

How to Approach the Question

First, identify the keywords 'successive discounts'. This is a crucial clue that the discounts are applied one after another on the remaining amount, not summed up.
Recognize the common trap: do not add the percentages (25 + 15 + 12.5). This is incorrect.
For each discount percentage 'd', convert it to a decimal and calculate the remaining factor as (1 - d). The factors are (1 - 0.25), (1 - 0.15), and (1 - 0.125).
Calculate the individual remaining factors: 0.75, 0.85, and 0.875.
Multiply these factors together to find the final price factor: 0.75 × 0.85 × 0.875.
Calculate the final result of the multiplication: 0.5578125. This is the portion of the original price that remains.

Concept Tested & Keywords

Concept Tested: Calculation of successive percentage discounts
Stem keywords: total discount, successive discounts, 25 percent, 15 percent, 12.5 percent
Lead-in keywords: What is

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