Question

If the price of sugar increases by 25%, by what percentage must a household reduce consumption to keep the expenditure the same?

• A. 20%
• B. 25%
• C. 15%
• D. 30%

Hint:

Shortcut formula for such questions: \[ \text{Reduction %} = \frac{\text{Price Increase %}}{100 + \text{Price Increase %}} \times 100 \] Example: \[ \text{If price increases by }25% \] \[ \text{Required reduction} = \frac{25}{125} \times 100 = 20% \] Memory trick: \[ \textbf{Price ↑ → Consumption ↓} \] To keep expenditure constant, consumption must decrease proportionally.

Answer 1

The Correct Option is A

Concept:
When the price of a commodity increases but the total expenditure must remain constant, the quantity consumed must decrease proportionally. This relationship can be calculated using the formula: \[ \text{Required Reduction in Consumption (%)} = \frac{\text{Increase in Price}}{100 + \text{Increase in Price}} \times 100 \] This formula helps determine how much consumption must be reduced so that the total spending does not change despite the price increase.
Step 1: Identify the given information.
\[ \text{Increase in price} = 25% \]
Step 2: Apply the formula.
\[ \text{Reduction in consumption} = \frac{25}{100 + 25} \times 100 \] \[ = \frac{25}{125} \times 100 \] \[ = 20% \]
Step 3: Alternative explanation using numbers.
Assume initially: \[ \text{Price of sugar} = ₹100 \text{ per unit} \] \[ \text{Quantity purchased} = 1 \text{ unit} \] \[ \text{Total expenditure} = ₹100 \] After a 25% increase: \[ \text{New price} = 100 + 25 = ₹125 \] To keep the expenditure ₹100: \[ \text{Quantity that can be purchased} = \frac{100}{125} = 0.8 \] Reduction in consumption: \[ 1 - 0.8 = 0.2 = 20% \]
Step 4: Selecting the correct answer.
\[ \boxed{20%} \]