The price of oil is increased by 25%. If the expenditure is not allowed to increase, the ratio between the reduction in consumption and the original consumption is

### Concept & Formula This problem centers on the inverse relationship between price and consumption when expenditure is held constant. Expenditure is the product of Price and Consumption: $$ \text{Expenditure} = \text{Price} \times \text{Consumption} $$ If Expenditure remains constant, any fractional increase in Price requires a specific fractional decrease in Consumption to maintain balance. ### Step-by-Step Solution 1. **Assume Initial Values:** Let the original price of oil be $100$ units and the original consumption be $100$ units. 2. **Calculate Initial Expenditure:** $$ \text{Expenditure} = 100 \times 100 = 10000 $$ 3. **Determine New Price:** The price increases by $25\%$, making the new price $125$. 4. **Find New Consumption:** Since expenditure must stay at $10000$, divide it by the new price. $$ \text{New Consumption} = \frac{10000}{125} = 80 $$ 5. **Calculate the Reduction:** $$ \text{Reduction in Consumption} = 100 - 80 = 20 $$ 6. **Find the Required Ratio:** The question asks for the ratio of the *reduction* to the *original* consumption. $$ \text{Ratio} = \frac{20}{100} = \frac{1}{5} $$ Expressed as a ratio, this is $1 : 5$. ### Exam Strategy & Shortcut Use the fraction method. A $25\%$ increase in price is equivalent to an increase of $+ \frac{1}{4}$. To find the required reduction fraction to keep expenditure constant, keep the numerator the same, and add the numerator to the denominator: $\frac{1}{4 + 1} = \frac{1}{5}$. This fraction $\frac{1}{5}$ directly represents the (Reduction / Original Consumption). Thus, the ratio is immediately $1 : 5$ without calculating any hypothetical totals. ### Common Pitfall A major trap is calculating the correct reduction ($20$) but finding the wrong ratio. Students often quickly write the ratio of "reduction to *new* consumption" ($20 : 80 = 1 : 4$) or "new to old consumption" ($80 : 100 = 4 : 5$). Always double-check exactly which two elements the question asks you to compare. ### Final Answer **Therefore, the correct answer is $1 : 5$.**