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 number of vehicles in the city of 'Punjab' is 25% less than the number of vehicles in the city of 'Pune', what is the percentage of motorcycles among the total number of vehicles in Pune?

### Concept & Relative Percentage When a quantity is given as a percentage less than another unknown quantity, you can use the known value to reverse-calculate the total base. $$ \text{Value}_1 = (100\% - P\%) \times \text{Value}_2 $$ ### Step-by-Step Solution * **Given:** Total vehicles in Punjab = 900. The number of cars in Pune = 480. * **Calculation:** Punjab's total vehicles are 25% less than Pune's total vehicles. * Let Pune's total vehicles be $P$. * $900 = P - 0.25P = 0.75P$ * $P = \frac{900}{0.75} = 1200$. So, total vehicles in Pune = 1200. * **Deduction:** Number of motorcycles in Pune = Total vehicles in Pune - Number of cars in Pune * Motorcycles in Pune = $1200 - 480 = 720$. * **Percentage Calculation:** Percentage of motorcycles in Pune = $(\frac{720}{1200}) \times 100$ * Percentage = $0.6 \times 100 = 60\%$. ### Exam Strategy & Shortcut Recognize that "25% less" means 75% or $\frac{3}{4}$. If $\frac{3}{4}$ of Pune is 900, then $\frac{1}{4}$ is 300, making the total for Pune 1200. Subtracting the 480 cars leaves 720 motorcycles. $720$ out of $1200$ easily simplifies to $\frac{72}{120}$ or $\frac{6}{10}$, which is $60\%$. ### Common Pitfall A frequent error is calculating 25% of Punjab's vehicles and adding it to 900. The 25% difference is based on Pune's unknown total, not Punjab's total. ### Final Answer Therefore, the correct answer is **60%**.