A dress shop marked down all items as following: | Group | Regular price | Sale price | | - | - | - | | A | ₹ 65 | ₹ 55 | | B | ₹ 60 | ₹ 50 | | C | ₹ 70 | ₹ 60 | | D | ₹ 75 | ₹ 65 | Which group of items was offered at the greatest rate of discount?

### Concept & Comparing Fractions The rate of discount is the absolute discount amount divided by the regular price. When comparing fractions with the same numerator, the fraction with the smallest denominator has the greatest overall value. $$ \text{Rate of Discount} = \frac{\text{Regular Price} - \text{Sale Price}}{\text{Regular Price}} $$ ### Step-by-Step Solution * First, calculate the absolute discount for each group: * Group A: $65 - 55 = 10$ * Group B: $60 - 50 = 10$ * Group C: $70 - 60 = 10$ * Group D: $75 - 65 = 10$ * The absolute discount is ₹ 10 for all groups. * Next, setup the fractions for the rate of discount: * Group A: $\frac{10}{65}$ * Group B: $\frac{10}{60}$ * Group C: $\frac{10}{70}$ * Group D: $\frac{10}{75}$ * Since the numerators are all identical (10), we only need to compare the denominators to find the largest value. * The smallest denominator is 60 (Group B). Therefore, $\frac{10}{60}$ is the largest fraction. * $\frac{10}{60} = \frac{1}{6} \approx 16.67\%$. ### Exam Strategy & Shortcut Notice immediately that the price drop is ₹ 10 across the board. A fixed price drop always represents a higher percentage impact on a smaller base price. Simply find the lowest regular price, which is ₹ 60 (Group B). ### Common Pitfall A student might instinctively look for the lowest sale price or the highest regular price, or they might waste time calculating the exact percentage for every single group instead of just comparing the fractions logically. ### Final Answer Therefore, the correct answer is **B**.