A watch is sold at a profit of $20\%$. If both the cost price and the selling price of the watch are decreased by ₹ 100, the profit would be $5\%$ more. Original cost price of the watch is (A.A.O. Exam, 2010)

### Concept & Absolute Value Changes in Profit and Loss When a fixed absolute amount is deducted from both CP and SP, the profit percentage changes. Set up the foundational equation linking the updated CP and SP. ### Step-by-Step Solution * Let original $CP = x$. * Original Profit = $20\%$, so Original $SP = 1.2x$. * Both CP and SP decrease by ₹ 100: * New $CP = x - 100$ * New $SP = 1.2x - 100$ * The new profit is $5\%$ more, meaning it is $20\% + 5\% = 25\%$. * Set up the equation: $\text{New SP} = \text{New CP} \times 1.25$ * $1.2x - 100 = (x - 100) \times 1.25$ * $1.2x - 100 = 1.25x - 125$ * $1.25x - 1.2x = 125 - 100$ * $0.05x = 25$ * $x = \frac{25}{0.05} = \frac{2500}{5} = 500$ ### Exam Strategy & Shortcut Use the ratio method. Initial CP : SP = 100 : 120 = 5 : 6. New Profit = 25%, so New CP : SP = 100 : 125 = 4 : 5. Both decreased by 100. Initial ratio: 5x, 6x. $\frac{5x - 100}{6x - 100} = \frac{4}{5}$ Cross multiply: $25x - 500 = 24x - 400 \implies x = 100$. Original CP = 5x = 5(100) = 500. This avoids decimals entirely. ### Common Pitfall Assuming "profit would be $5\%$ more" means the new profit is $5\%$ of CP, rather than interpreting it as the old percentage plus $5\%$ (i.e., $25\%$). ### Final Answer Therefore, the correct answer is **₹ 500**.