After successive discounts of $12\%$ and $5\%$ an article was sold for ₹ $209$. What was the original price of the article?

### Concept & Formula To find the original Marked Price (MP) given the final Selling Price (SP) and multiple successive discounts, reverse the percentage reductions using multipliers. $$ \text{MP} = \frac{\text{SP}}{\left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right)} $$ ### Step-by-Step Solution * **Given:** * Selling Price = ₹ $209$ * First discount = $12\%$ * Second discount = $5\%$ * **Calculation:** * Let the original price be $x$. * $x \times (1 - 0.12) \times (1 - 0.05) = 209$ * $x \times 0.88 \times 0.95 = 209$ * $0.88 \times 0.95 = 0.836$. So, $x \times 0.836 = 209$. * $x = \frac{209}{0.836} = \frac{209000}{836} = 250$. ### Exam Strategy & Shortcut Calculate the single equivalent discount: $12 + 5 - (12 \times 5)/100 = 17 - 0.6 = 16.4\%$. This means the selling price is $(100 - 16.4)\% = 83.6\%$ of the original price. $83.6\% = 209 \Rightarrow 1\% = \frac{209}{83.6} = 2.5$. Thus $100\% = 250$. ### Common Pitfall Attempting to add the discounts ($12 + 5 = 17\%$) and saying the price is $83\%$ of the original, which gives an incorrect original price of roughly $251.8$. ### Final Answer Therefore, the correct answer is **₹ 250**.