If the price of oil is increased by 30%, then by how much percent a family should reduce its consumption so that the expenditure would remain the same?

### Concept & Formula When overall expenditure must be kept constant, an increase in the price of a commodity forces a reduction in its consumption. We can determine the exact percentage reduction required using the constant product rule formula, where $R$ is the percentage increase in price: $$ \text{Reduction}\% = \left( \frac{R}{100 + R} \right) \times 100 $$ ### Step-by-Step Solution * **Given:** * Price increase ($R$) = $30\%$ * **Calculation:** 1. Substitute the value of $R$ into the formula: $$ \text{Required Reduction}\% = \left( \frac{30}{100 + 30} \right) \times 100 $$ 2. Add the denominator values: $$ = \left( \frac{30}{130} \right) \times 100 $$ 3. Simplify the fraction by canceling the common zero: $$ = \left( \frac{3}{13} \right) \times 100 $$ 4. Multiply and convert to a mixed fraction: $$ = \frac{300}{13} = 23 \frac{1}{13}\% $$ ### Exam Strategy & Shortcut Instead of writing out the formula, quickly visualize the ratio. If price goes from $100$ to $130$, consumption must drop from $130$ back down to $100$ to balance the equation. The drop is $30$ on a new base of $130$. This logic instantly yields $\frac{30}{130}$, which simplifies to $\frac{3}{13}$, avoiding the need for algebraic rote memorization. ### Common Pitfall Students often subtract $R$ in the denominator instead of adding it, confusing the formula for price reduction with the formula for price increase. Remember: an INCREASE in price means a LARGER denominator ($100 + R$), which results in a smaller consumption percentage. ### Final Answer **Therefore, the correct answer is $23 \frac{1}{13}\%$.**