Direction: Study the following data carefully and answer the questions accordingly. The given table shows data regarding the total number of vehicles (cars + motorcycles) in five different cities. It also displays the percentage/ number of cars and the percentage of motorcycles in each city relative to the total number of vehicles in that city. Some of the data is missing from the table. You need to calculate the missing data and answer the questions based on it. | Cities | Total number of vehicles in the cities | Percentage/ number of cars in the city | Percentage of motorcycles in the city | |---|---|---|---| | Pune | ___ | 480 | ___ | | Delhi | ___ | 600 | 25% | | Jaipur | ___ | 30% | ___ | | Punjab | 900 | ___ | ___ | | Haryana | ___ | ___ | 60% | Let '$a$' represent the difference between the number of cars and motorcycles in the city of 'Jaipur,' and '$b$' represent the total number of vehicles in the city of 'Jaipur.' Which of the following options accurately expresses the relationship between '$a$' and '$b$'?

### Concept & Percentage Breakdown The total number of vehicles in a city is the sum of cars and motorcycles (which represents 100%). By determining the missing percentage of motorcycles, we can find the percentage difference between the two vehicle types. ### Step-by-Step Solution * **Given:** In Jaipur, cars account for 30% of the total vehicles. * **Calculation:** Since total vehicles = 100%, the percentage of motorcycles in Jaipur = $100\% - 30\% = 70\%$. * **Deduction:** The difference between the number of cars and motorcycles is given by '$a$', and total vehicles by '$b$'. * Percentage difference = $70\% - 30\% = 40\%$. * This means the absolute difference '$a$' is 40% of the total vehicles '$b$'. * Formulating the equation: $a = 40\% \times b$ * $a = \frac{40}{100} \times b$ * $a = \frac{2}{5} \times b$ * Multiplying both sides by 5: $5a = 2b$. (Note: $5a - 2b = 0$ is also mathematically equivalent). ### Exam Strategy & Shortcut Whenever dealing with simple percentage splits (like 30% and 70%), calculate the difference in percentages immediately ($40\%$). Convert that difference to a fraction ($40\% = \frac{2}{5}$) to quickly establish the ratio $a = \frac{2}{5}b$, leading straight to $5a = 2b$. ### Common Pitfall A common mistake is adding the percentages or calculating 30% of 70% instead of finding their difference relative to the total 100%. ### Final Answer Therefore, the correct answer is **$5a = 2b$**.