By selling an article, Michael earned a profit equal to one-fourth of the price he bought it. If he sold it for ₹ 375, what was the cost price?

### Concept & Fractional Profit Equations Similar to fractional losses, when profit is described as a fraction of the cost price, it establishes a direct algebraic relationship. The selling price is simply the cost price plus that fractional profit. $$ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} $$ ### Step-by-Step Solution * Let the Cost Price (CP) of the article be $x$. * Given: Selling Price (SP) = ₹ 375. * Given: Profit = one-fourth of Cost Price = $\frac{1}{4}x$. * Use the fundamental formula: $SP = CP + \text{Profit}$. * Substitute the values: $375 = x + \frac{1}{4}x$. * Combine the terms on the right: $375 = \frac{5}{4}x$. * Isolate $x$: $x = 375 \times \frac{4}{5}$. * Calculate: $375 \div 5 = 75$. * Multiply: $75 \times 4 = 300$. * The Cost Price is ₹ 300. ### Exam Strategy & Shortcut Profit is $1/4$ of CP, which means Profit is $25\%$. A $25\%$ profit means the item is sold for $125\%$ of its CP, or $5/4$ of CP. $SP = \frac{5}{4} CP = 375$. $CP = 375 \times \frac{4}{5} = 300$. Familiarity with standard percentage fractions ($25\% = 1/4 \rightarrow SP = 5/4 CP$) makes this mental math. ### Common Pitfall Subtracting one-fourth of 375 from 375 to find the cost price (which would incorrectly yield 281.25). You cannot calculate the profit amount by applying the profit fraction to the Selling Price; it must be applied to the Cost Price. ### Final Answer Therefore, the correct answer is **₹ 300**.