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.

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Concept & Formula: There is a direct proportional relationship between Marked Price (MP), Cost Price (CP), Profit%, and Discount%: (MP/CP) = (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: (1150/CP) = (100 + 15/100 - 15) (1150/CP) = (115/85) 3. Solve for CP: CP = (1150 × 85/115) CP = 10 × 85 = 850 Exam Strategy & Shortcut: Using the formula (MP/CP) = (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.

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