Sanjay made a profit of 8% by selling a shirt after offering a discount of 12%. If the marked price of the shirt is ₹ 1080, find its cost price.

### Concept & Formula There is a direct proportional relationship linking Marked Price (MP), Cost Price (CP), Discount percentage, and Profit percentage: $$\frac{MP}{CP} = \frac{100 + \text{Profit}\%}{100 - \text{Discount}\%}$$ ### Step-by-Step Solution 1. Identify the given values: Marked Price ($MP$) = ₹ $1080$, Discount = $12\%$, Profit = $8\%$. 2. We need to find the Cost Price ($CP$). 3. Substitute the values into the direct formula: $$\frac{1080}{CP} = \frac{100 + 8}{100 - 12}$$ $$\frac{1080}{CP} = \frac{108}{88}$$ 4. Simplify the fraction on the right side: $$\frac{108}{88} = \frac{27}{22}$$ 5. Solve for $CP$: $$\frac{1080}{CP} = \frac{27}{22}$$ $$CP = \frac{1080 \times 22}{27}$$ $$CP = 40 \times 22 = 880$$ ### Exam Strategy & Shortcut Instead of calculating the Selling Price first ($1080 \times 0.88 = 950.4$) and then dividing by the profit multiplier ($950.4 / 1.08 = 880$), using the direct ratio formula $\frac{MP}{CP} = \frac{100+P}{100-D}$ allows for rapid mental calculation and fraction simplification. ### Common Pitfall A common mistake is calculating the $8\%$ profit based on the Marked Price rather than the Cost Price, which breaks the fundamental rule of profit and loss. ### Final Answer Therefore, the correct answer is **880**.