The price of a cycle is marked at ₹ 1150. A shopkeeper earns a profit of 15% after allowing a discount of 15% on the marked price. Find the cost price of the cycle.

### Concept & Formula There is a direct proportional relationship between Marked Price (MP), Cost Price (CP), Profit%, and Discount%: $$\frac{MP}{CP} = \frac{100 + Profit\%}{100 - Discount\%}$$ ### Step-by-Step Solution 1. Identify the given values: Marked Price ($MP$) = ₹ 1150 Profit = $15\%$ Discount = $15\%$ 2. Use the direct ratio formula: $$\frac{1150}{CP} = \frac{100 + 15}{100 - 15}$$ $$\frac{1150}{CP} = \frac{115}{85}$$ 3. Solve for CP: $$CP = \frac{1150 \times 85}{115}$$ $$CP = 10 \times 85 = 850$$ ### Exam Strategy & Shortcut Using the formula $\frac{MP}{CP} = \frac{100+P}{100-D}$ is the fastest way. The numbers 115 and 85 immediately simplify against the 1150 MP. ### Common Pitfall Assuming that a $15\%$ profit and $15\%$ discount cancel each other out, making the CP equal to the MP. They are applied to different bases. ### Final Answer Therefore, the correct answer is **₹ 850**.