If a man reduces the selling price of a fan from ₹ 400 to ₹ 380, his loss increases by $2\%$. The cost price of the fan is

### Concept & Proportional Difference in Loss Just like profit, any change in loss percentage directly correlates to the absolute change in the Selling Price (SP). Both refer to the same baseline Cost Price (CP). $$ \Delta \text{SP} = (\Delta \text{Loss \%}) \times \text{CP} $$ ### Step-by-Step Solution * Given: * Original Selling Price ($\text{SP}_1$) = ₹ 400 * Reduced Selling Price ($\text{SP}_2$) = ₹ 380 * Increase in loss percentage = $2\%$ * Find the reduction in Selling Price: * Difference in SP = $400 - 380 = \text{₹ 20}$ * This ₹ 20 drop directly caused the loss to increase by $2\%$. Therefore, $2\%$ of the Cost Price is exactly equal to ₹ 20. * $2\%$ of CP = 20 * $\frac{2}{100} \times \text{CP} = 20$ * Solve for CP: * $\text{CP} = \frac{20 \times 100}{2}$ * $\text{CP} = 10 \times 100 = 1000$ * The actual cost price of the fan is ₹ 1000. Let's check the options provided. * Options given: (a) ₹ 480, (b) ₹ 500, (c) ₹ 600, (d) None of these. * Since ₹ 1000 is not present in options (a), (b), or (c), the correct choice is "None of these". ### Exam Strategy & Shortcut Mental math is the fastest route here. The price dropped by 20. This drop equates to a $2\%$ loss. If $2\% \rightarrow 20$, then $1\% \rightarrow 10$. The full Cost Price is $100\%$, so $100\% \rightarrow 100 \times 10 = 1000$. ### Common Pitfall A frequent error is trying to formulate complex equations involving initial loss percentages (e.g., $L\%$). Since the *change* in loss directly links to the *change* in price, the initial loss percentage is completely irrelevant and unnecessary to find. ### Final Answer Therefore, the correct answer is **None of these**.