The marks scored in an examination are converted from 50 to 10 for the purpose of internal assessment. The highest marks were 47 and the lowest were 14. The difference between the maximum and the minimum internal assessment scores is

### Concept & Formula When marks are scaled or converted from a base scale ($S_1$) to a new scale ($S_2$), the scaling factor is constant. $$\text{Scaling Factor} = \frac{\text{New Maximum}}{\text{Old Maximum}} = \frac{10}{50} = \frac{1}{5} = 0.2$$ The difference between two values on the new scale is equal to their difference on the old scale multiplied by this scaling factor. $$\text{New Difference} = \text{Old Difference} \times \text{Scaling Factor}$$ ### Step-by-Step Solution * **Calculate the difference on the original scale:** $$\text{Old Maximum} = 47$$ $$\text{Old Minimum} = 14$$ $$\text{Old Difference} = 47 - 14 = 33$$ * **Apply the scaling factor:** $$\text{New Difference} = 33 \times \frac{10}{50}$$ $$\text{New Difference} = 33 \times 0.2 = 6.6$$ ### Exam Strategy & Shortcut Instead of converting the maximum score ($47 \times 0.2 = 9.4$) and minimum score ($14 \times 0.2 = 2.8$) individually and subtracting them, subtract first to deal with a single operation: $$47 - 14 = 33$$ $$33 \div 5 = 6.6$$ This halves your arithmetic computation and reduces chances of errors. ### Common Pitfall Accidentally scaling by inverted fractions (like $\frac{50}{10} = 5$) or unnecessarily complicating the formula by computing individual scaled boundaries with rounding errors. ### Final Answer **Therefore, the correct answer is 6.6.**