1. **State the problem:** A shirt has a marked price (m.p) of 800. A discount of 13% is given to the customer, and the trader makes a profit of 20%. We need to find the cost price (how much the trader paid for the shirt). 2. **Formulas and rules:** - Selling Price (S.P) after discount = Marked Price - Discount - Discount = (Discount % of Marked Price) = $\frac{13}{100} \times 800$ - Profit % = $\frac{S.P - Cost Price}{Cost Price} \times 100$ 3. **Calculate the discount amount:** $$\text{Discount} = \frac{13}{100} \times 800 = 104$$ 4. **Calculate the selling price:** $$S.P = 800 - 104 = 696$$ 5. **Use profit formula to find cost price (C.P):** $$20 = \frac{696 - C.P}{C.P} \times 100$$ 6. **Rewrite the equation:** $$0.20 = \frac{696 - C.P}{C.P}$$ 7. **Multiply both sides by $C.P$:** $$0.20 \times C.P = 696 - C.P$$ 8. **Bring all terms to one side:** $$0.20 C.P + C.P = 696$$ 9. **Combine like terms:** $$1.20 C.P = 696$$ 10. **Solve for $C.P$:** $$C.P = \frac{696}{1.20}$$ 11. **Simplify the fraction:** $$C.P = \frac{\cancel{696}}{\cancel{1.20}} = 580$$ **Final answer:** The trader paid 580 for the shirt.