Jacob bought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of ₹ 1100. How much did he spend on repairs if he made a profit of 20%?

### Concept & Base Cost Logic In profit and loss, "Cost" refers to the initial purchase price, and the "Total Cost Price" includes the purchase price plus repair overheads. Profit is calculated on the Total Cost Price. ### Step-by-Step Solution * **Define Variables:** * Let the original purchase cost of the scooter be $C$. * Cost of repairs = $10\%$ of $C = 0.10C$. * Total Cost Price ($\text{CP}_{\text{total}}$) = Purchase Cost + Repair Cost = $C + 0.10C = 1.10C$. * **Relate Profit Percentage to Profit Value:** * Given Profit % = $20\%$. * Given Actual Profit = ₹ 1100. * We know: $\text{Profit} = \text{Profit \%} \times \text{CP}_{\text{total}}$ * $1100 = 0.20 \times 1.10C$ * $1100 = 0.22C$ * **Solve for the Unknowns:** * $C = \frac{1100}{0.22} = \frac{110000}{22} = 5000$. * The original purchase cost is ₹ 5000. * The amount spent on repairs is $10\%$ of ₹ 5000 = ₹ 500. ### Exam Strategy & Shortcut Work directly with ratios. The total cost represents $110\%$ of the initial price. The profit is $20\%$ of this total cost, which equals $22\%$ of the initial price ($1.1 \times 0.2 = 0.22$). If $22\%$ equals 1100, then $10\%$ (the repair cost) is strictly proportional. $\frac{1100}{22} \times 10 = 50 \times 10 = 500$. ### Common Pitfall A common error is confusing the initial purchase cost with the total investment (which includes repairs). If you calculate $20\%$ profit on $C$ alone instead of $1.1C$, you will get incorrect numbers. ### Final Answer Therefore, the correct answer is **₹ 500**.