Tarun got 30% concession on the labelled price of an article and sold it for ₹ 8750 with 25% profit on the price he bought. What was the labelled price?

### Concept & Chained Ratios The final Selling Price is a result of a chained multiplication of the Labelled Price (MP) adjusted by the discount and then the profit margin. $$ \text{SP} = \text{MP} \times (1 - \text{Discount \%}) \times (1 + \text{Profit \%}) $$ ### Step-by-Step Solution * Let the labelled price of the article be $x$. * Tarun received a 30% concession (discount). * Tarun's Cost Price (CP) = $x \times (1 - 0.30) = 0.70x$. * He sold it for ₹ 8750, making a 25% profit on his Cost Price. * Selling Price (SP) = $\text{CP} \times (1 + 0.25) = 0.70x \times 1.25$. * We are given that $\text{SP} = 8750$. * Therefore, $0.70x \times 1.25 = 8750$. * $0.875x = 8750$. * $x = \frac{8750}{0.875} = 10000$. ### Exam Strategy & Shortcut Work backwards using multipliers. Final SP = 8750. Profit was 25% (multiplier of $\frac{5}{4}$). To reverse this to find CP, multiply by $\frac{4}{5}$: $\text{CP} = 8750 \times \frac{4}{5} = 7000$. Discount was 30% (multiplier of 0.7 or $\frac{7}{10}$). To reverse this to find MP, multiply by $\frac{10}{7}$: $\text{MP} = 7000 \times \frac{10}{7} = 10000$. ### Common Pitfall Calculating the 25% profit on the labelled price rather than the price Tarun actually paid for the article. ### Final Answer Therefore, the correct answer is **₹ 10,000**.