Find the selling price of an article if a shopkeeper allows two successive discounts of $5\%$ each on the marked price of ₹ $80$. (C.B.I., 2003)

### Concept & Logic When identical successive discounts are applied, the final selling price can be calculated by applying the discount multiplier repeatedly to the marked price. $$ \text{Selling Price} = \text{Marked Price} \times \left(1 - \frac{r}{100}\right)^2 $$ ### Step-by-Step Solution * **Given:** * Marked Price = ₹ $80$ * First discount = $5\%$ * Second discount = $5\%$ * **Calculation:** * Find the price after the first $5\%$ discount: $5\%$ of $80 = \frac{5}{100} \times 80 = 4$. Price after 1st discount = $80 - 4 = ₹ 76$. * Find the price after the second $5\%$ discount on the new price: $5\%$ of $76 = \frac{5}{100} \times 76 = \frac{380}{100} = 3.80$. Final Selling Price = $76 - 3.80 = ₹ 72.20$. ### Exam Strategy & Shortcut Instead of step-by-step subtraction, you can combine the discounts. Two $5\%$ discounts combine to: $5 + 5 - \frac{5 \times 5}{100} = 10 - 0.25 = 9.75\%$. The final price is $(100 - 9.75)\% = 90.25\%$ of ₹ $80$. $80 \times 0.9025 = 72.20$. Alternatively, use the first method as the numbers (like $5\%$ of $80$) are very simple to compute mentally. ### Common Pitfall A common arithmetic error happens when calculating the $5\%$ of $76$. Make sure to place the decimal point correctly: $76 \times 5 = 380$, divided by $100$ is $3.80$. ### Final Answer Therefore, the correct answer is **₹ 72.20**.