If the area of a rectangular plot increases by 30% while its breadth remains the same, what will be the ratio of the areas of new and old figures?

### Concept & Proportionality When comparing two values where one is a percentage increase of the other, their ratio can be found directly by comparing their relative percentage bases. $$ \text{Ratio} = \frac{\text{New Value}}{\text{Old Value}} $$ ### Step-by-Step Solution * Let the area of the old figure be 100 units. * The area increases by 30%, meaning the new area is $100 + 30 = 130$ units. * The question asks for the ratio of the areas of the **new** and **old** figures. $$ \text{Ratio} = \frac{\text{New Area}}{\text{Old Area}} = \frac{130}{100} $$ * Simplify the fraction by dividing by 10: $$ \text{Ratio} = \frac{13}{10} = 13 : 10 $$ * Check the provided options: (a) 1:3, (b) 3:1, (c) 4:7, (d) 10:13. * The correct ratio $13 : 10$ is not listed among the first four options (Note that option d is the reverse ratio). ### Exam Strategy & Shortcut Read the required order carefully: "new and old". Old is 100%, New is 130%. The ratio is simply $130 : 100 \rightarrow 13 : 10$. If you see $10 : 13$ as an option, recognize it as a trap for those who read "old and new" instead. ### Common Pitfall Selecting option (d) 10 : 13 because it contains the correct numbers, failing to notice that the order of the ratio requested is New : Old, not Old : New. ### Final Answer Therefore, the correct answer is **None of these**.