Question : The price of sugar increases by 15%. By what percentage should the consumption of sugar be decreased so that the expenditure on the purchase of sugar remains the same? [Give your answer correct to 2 decimal places.]
Option 1: 11.11%
Option 2: 12.5%
Option 3: 14.16%
Option 4: 13.04%
Correct Answer: 13.04%
Solution :
Given that the price of sugar is raised by 15%
Price = $\frac{\text{Expenditure}}{\text{Consumption}}$
Let the original price be 100x
New price after increase in price = $100\text{x}+ 100\text{x} \times \frac{15}{100}$ = 115x
As expenditure remains same.
Then, $\frac{\text{New consumption}}{\text{Original consumption}} = \frac{\text{Original Price}}{\text{New price}} = \frac{100\text{x}}{115\text{x}}$
⇒ $\frac{\text{New consumption}}{\text{Original consumption}} = \frac{20}{23}$
Reduction in consumption = (23 - 20) = 3
Reduction in percentage = $\frac{3}{23} \times 100$ = 13.04%.
Hence, the correct answer is 13.04%.
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