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% | Suppose the ratio of the number of cars in cities 'Jaipur' and 'Punjab' is 5 : 9, and the difference between the number of motorcycles in city 'Jaipur' and 'Punjab' is 340, what is the total number of vehicles in city 'Jaipur'?

### Concept & Algebraic Formulation Use given ratios to connect variables across different groups. By establishing a single variable (e.g., total vehicles in Jaipur), you can express all other quantities in terms of that variable and solve using the given absolute difference. ### Step-by-Step Solution * **Given:** Total vehicles in Punjab = 900. Cars in Jaipur constitute 30% of Jaipur's total. Ratio of cars in Jaipur to Punjab = 5:9. Difference in motorcycles between Jaipur and Punjab = 340. * Let the total number of vehicles in Jaipur be $x$. * **Calculation (Jaipur):** Cars = $0.3x$, Motorcycles = $0.7x$. * **Calculation (Punjab):** The ratio of cars in Jaipur to Punjab is 5:9. * Cars in Punjab = $(\frac{9}{5}) \times (\text{Cars in Jaipur}) = (\frac{9}{5}) \times 0.3x = 1.8 \times 0.3x = 0.54x$. * Since total vehicles in Punjab = 900, Motorcycles in Punjab = $900 - \text{Cars in Punjab} = 900 - 0.54x$. * **Deduction:** The difference between motorcycles in Jaipur and Punjab is 340. * Absolute difference: $|0.7x - (900 - 0.54x)| = 340$ * Case 1: $0.7x + 0.54x - 900 = 340 \implies 1.24x = 1240 \implies x = 1000$. * Case 2: $900 - 0.54x - 0.7x = 340 \implies 1.24x = 560 \implies x = 451.61$ (Since vehicles must be an integer, this is invalid). * Thus, $x = 1000$. ### Exam Strategy & Shortcut Whenever a ratio links a percentage-based variable to a fixed total (like Punjab's 900), express the unknown components strictly in terms of a single variable $x$ (Jaipur total). Setting up the final algebraic difference equation guarantees the exact integer value for $x$. ### Common Pitfall A common pitfall is incorrectly assigning the ratio 5:9 to the total vehicles instead of the number of cars, which skews the entire algebraic setup. ### Final Answer Therefore, the correct answer is **1000**.