If the price of tea is increased by 20%, by how much percent must the consumption of tea be diminished so as not to increase the expenditure?

Appeared in: RRB Staff Nurse Jaipur-6th June 2018

Explanation

The core principle is that if total expenditure is to remain constant, price and consumption are inversely proportional.
A 20% increase in price is equivalent to multiplying the original price by 1.2 or 6/5.
To counteract this and keep the product (expenditure) the same, the consumption must be multiplied by the reciprocal, which is 5/6.
A reduction to 5/6 of the original value means the decrease is 1 - 5/6 = 1/6 of the original consumption.
Converting the fractional decrease to a percentage gives (1/6) × 100 = 16.66...%, which is expressed as the mixed fraction 16 2/3%.

Option A: This is an incorrect calculation. A 14 2/3% decrease would correspond to a price increase of approximately 17.2%.
Option B: This is an incorrect calculation. An 18 1/3% decrease would be the result if the price had increased by 22.4%.
Option D: This is an incorrect calculation. A 14 1/3% decrease would correspond to a price increase of approximately 16.7%.

Visual 1: Formula Card - A card displaying the formula for constant expenditure problems: % Decrease in Consumption = [R / (100 + R)] × 100, where R is the percentage increase in price.
Visual 2: Infographic - An infographic showing a balance scale. On one side, 'Price' is shown increasing, and on the other side, 'Consumption' is shown decreasing to keep the 'Expenditure' level balanced.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Application of percentages in problems involving constant expenditure as background academic context rather than a clinical decision trigger.
Personal Budgeting: This concept is crucial for managing household finances. If the price of a commodity like petrol increases, one must reduce its consumption to keep the monthly fuel budget the same.
Business Pricing: Companies use this principle to analyze the impact of price changes on sales volume and overall revenue.
What if? If the price had decreased by 20%, the consumption could be increased while keeping the expenditure constant. The formula would be % Increase = [R / (100 - R)] × 100. This would result in a [20 / (100 - 20)] × 100 = 25% increase in consumption.

How to Approach the Question

Step 1: Identify the core constraint: The total expenditure must not increase, meaning it remains constant.
Step 2: Recall the relationship: Expenditure = Price × Consumption. For a constant expenditure, price and consumption are inversely proportional.
Step 3: Apply the direct formula for this scenario. If price increases by R%, the required percentage decrease in consumption is [R / (100 + R)] × 100.
Step 4: Substitute the given price increase, R = 20, into the formula: [20 / (100 + 20)] × 100.
Step 5: Simplify the fraction: 20 / 120 = 1/6.
Step 6: Calculate the percentage: (1/6) × 100 = 16.66...%, which is equal to the mixed fraction 16 2/3%.

Concept Tested & Keywords

Concept Tested: Application of percentages in problems involving constant expenditure.
Stem keywords: price, increased by 20%, consumption, diminished, expenditure
Lead-in keywords: how much percent
Negative lead-in flag: false

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