The sale price of an article including the sales tax is ₹ 1232. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is

### Concept & Logic The final sale price paid by a customer is built upon successive percentage increases: first, the shopkeeper marks up the Cost Price to get their desired Selling Price (via profit), and then the government adds sales tax onto that Selling Price. ### Step-by-Step Solution 1. **Find the actual Selling Price (excluding tax):** Let the selling price before tax be $SP$. Sales tax is $10\%$ on this $SP$. Final price including tax = $SP + 10\% \text{ of } SP = 1.10 \times SP$. Given final price = ₹ $1232$. $$1.10 \times SP = 1232$$ $$SP = \frac{1232}{1.10} = 1120$$ So, the shopkeeper receives ₹ $1120$ for the article. 2. **Find the Cost Price (CP):** The shopkeeper makes a $12\%$ profit on the $CP$ to reach the $SP$ of ₹ $1120$. $$SP = CP \times \left(1 + \frac{12}{100}\right)$$ $$1120 = CP \times 1.12$$ $$CP = \frac{1120}{1.12}$$ Multiply by 100 to remove decimals: $$CP = \frac{112000}{112} = 1000$$ ### Exam Strategy & Shortcut Chain the multipliers backward in a single equation. Let $CP$ be $x$. $x \times (\text{Profit Multiplier}) \times (\text{Tax Multiplier}) = \text{Final Price}$ $x \times 1.12 \times 1.10 = 1232$ $x \times 1.232 = 1232$ $x = 1000$. ### Common Pitfall A frequent error is calculating the $10\%$ sales tax on the base Cost Price rather than the intermediate Selling Price. Tax is always applied to the transaction value at the register. ### Final Answer Therefore, the correct answer is **₹ 1000**.