For the purchase of a motor car, a man has to pay ₹ $17000$ when a single discount of $15\%$ is allowed. How much will he have to pay for it if two successive discounts of $5\%$ and $10\%$ respectively are allowed? (S.S.C., 2005)

### Concept & Logic To find the final price under a new discount scheme, you first need to determine the original Marked Price of the item using the initial selling price and discount data. $$ \text{Marked Price} = \frac{\text{Selling Price}}{1 - \frac{\text{Discount \%}}{100}} $$ ### Step-by-Step Solution * **Given:** * Selling Price 1 = ₹ $17000$ * Single discount = $15\%$ * Alternative discounts = $5\%$ and $10\%$ successively * **Calculation:** * First, find the Marked Price (MP). A $15\%$ discount means the buyer paid $85\%$ of the MP. $85\% \text{ of MP} = 17000$ $\text{MP} = \frac{17000}{0.85} = \frac{17000 \times 100}{85} = 200 \times 100 = ₹ 20000$. * Now, calculate the new selling price with successive discounts of $5\%$ and $10\%$ on the MP. * Apply the first discount of $5\%$ on ₹ $20000$: $5\%$ of $20000 = 1000$. Price = $20000 - 1000 = ₹ 19000$. * Apply the second discount of $10\%$ on ₹ $19000$: $10\%$ of $19000 = 1900$. New Selling Price = $19000 - 1900 = ₹ 17100$. ### Exam Strategy & Shortcut Find the equivalent single discount for $5\%$ and $10\%$: $5 + 10 - \frac{5 \times 10}{100} = 15 - 0.5 = 14.5\%$. The buyer pays $100\% - 14.5\% = 85.5\%$ of the Marked Price. Since $85\%$ of MP is $17000$, then $1\%$ of MP is $\frac{17000}{85} = 200$. Therefore, $85.5\%$ of MP is $85.5 \times 200 = 17100$. This avoids calculating the actual Marked Price directly. ### Common Pitfall A frequent mistake is assuming that successive discounts of $5\%$ and $10\%$ are exactly the same as a single discount of $15\%$, leading to the incorrect answer of ₹ $17000$. Successive discounts are always less advantageous to the buyer than a single combined discount. ### Final Answer Therefore, the correct answer is **₹ 17100**.