If the price of a medical textbook increases by 20%, by what percentage must the consumption be reduced so as not to increase the expenditure?

Appeared in: RML Lucknow - 2021

Explanation

The core principle is that if total expenditure must remain constant, price and consumption are inversely proportional.
A 20% increase in price means the new price is 1.2 times the original price.
To keep the product (Expenditure) constant, consumption must be divided by 1.2, which is equivalent to multiplying by 1/1.2 or 5/6.
A reduction to 5/6 of the original amount means the reduction itself is 1 - 5/6 = 1/6.
Converting 1/6 to a percentage gives (1/6) × 100 = 16.666...%, which is rounded to 16.67%.

Option A: This is a common error where one assumes the percentage reduction is the same as the percentage increase. However, the base for the percentage change is different in each case.
Option C: This value is incorrect for a price increase. A 25% reduction is too large and would result in a significant decrease in total expenditure.
Option D: This is a mathematically incorrect value for the given problem. A 10% reduction is not sufficient to offset a 20% price increase and would result in an overall increase in expenditure.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Percentage change and inverse proportion as background academic context rather than a clinical decision trigger.
While not a clinical question, the underlying concept of budgeting and resource management is a critical non-clinical skill for nurses, especially those in administrative or leadership roles.
Understanding how to adjust for cost increases is essential for managing departmental budgets, ordering supplies, and ensuring resources are allocated efficiently without overspending.
What if? If the price of a crucial medication increased by 15%, the hospital would need to reduce its consumption (or find cost savings elsewhere) by [15 / (100 + 15)] × 100 ≈ 13.04% to maintain the same budget line item.

How to Approach the Question

First, identify the core relationship: Expenditure = Price × Consumption.
Recognize that the problem requires the expenditure to remain constant, which implies an inverse relationship between price and consumption.
Recall or derive the formula for this specific scenario: Percentage Reduction = [R / (100 + R)] × 100, where R is the percentage increase in price.
Substitute the given value, R = 20, into the formula.
Calculate the result: [20 / (100 + 20)] × 100 = (20 / 120) × 100.
Simplify the fraction (20/120 = 1/6) and compute the final percentage: (1/6) × 100 ≈ 16.67%.

Concept Tested & Keywords

QJxZ3m0jMhwenm9dy8ySZt

Practise the full RML Lucknow - 2021

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