Step 1 : Understanding the Question
This problem involves the relationship between Price, Consumption, and Expenditure. When the price of a commodity (in this case, potatoes) increases, a consumer must reduce their usage (consumption) to maintain a fixed budget. The question asks for the specific percentage by which the consumption must be curtailed so that the total financial outlay remains at its original level.
Step 2 : Key Formulas and approach
The core concept is that $\text{Expenditure} = \text{Price} \times \text{Consumption}$. If the Expenditure is to remain constant, then Price and Consumption are inversely proportional. To calculate the necessary reduction, we determine how much of the "new price" represents the "increase" that needs to be offset.
Key Formula:
$\text{Percentage Reduction in Consumption} = \left( \frac{\text{Difference in Price}}{\text{New Price}} \right) \times 100$
Step 3 : Detailed Explanation
Identifying Price Points: We are given the original price of potatoes as Rs. 18 per kilogram and the inflated new price as Rs. 25 per kilogram.
Calculating the Absolute Increase: The price has increased by Rs. 7 ($25 - 18 = 7$). To keep the budget the same, the consumer needs to effectively "remove" Rs. 7 worth of potato consumption from every Rs. 25 they would now be expected to spend.
Determining the Ratio of Reduction: The reduction required is the ratio of the price increase to the new total price. This is represented by the fraction $\frac{7}{25}$.
Converting to Percentage: To convert this fraction into a percentage, we multiply by 100: $\text{Reduction %} = \frac{7}{25} \times 100$.
Final Computation: Since 25 goes into 100 four times, the equation simplifies to $7 \times 4$, which equals 28%. This means a 28% cut in quantity will keep the total spending unchanged.
Step 4 : Final Answer
The consumer must reduce potato usage by 28% to avoid any increase in expenditure, corresponding to option (A).