Calculating Total Petrol Cars from State Data

The question asks for the sum of petrol engine cars across four different states (A, B, C, and D) based on the provided table. The table gives the percentage distribution of the total cars in each state and the ratio of diesel engine cars to petrol engine cars for each state.

The total number of cars across all four states is given as 1400.

Step-by-Step Calculation of Petrol Cars per State

First, we need to find the total number of cars in each state using the percentage distribution. Then, for each state, we will use the given ratio of diesel to petrol cars to determine the number of petrol cars.

1. Calculate Total Cars in Each State

• State A: The percentage distribution is 14%.
  Total cars in State A = $\text{Total Cars} \times \frac{\text{Percentage for A}}{100}$
  Total cars in State A = $1400 \times \frac{14}{100} = 14 \times 14 = 196$ cars.
• State B: The percentage distribution is 28%.
  Total cars in State B = $1400 \times \frac{28}{100} = 14 \times 28 = 392$ cars.
• State C: The percentage distribution is 32%.
  Total cars in State C = $1400 \times \frac{32}{100} = 14 \times 32 = 448$ cars.
• State D: The percentage distribution is 26%.
  Total cars in State D = $1400 \times \frac{26}{100} = 14 \times 26 = 364$ cars.

Let's verify the total: $196 + 392 + 448 + 364 = 1400$. This matches the given total number of cars.

2. Calculate Petrol Cars in Each State

Now, we use the Diesel Engine Cars : Petrol Engine Cars ratio for each state.

• State A: Ratio is 3 : 4. Total parts in ratio = $3 + 4 = 7$. The fraction of petrol cars is $\frac{4}{7}$.
  Petrol cars in State A = Total cars in A $\times \frac{4}{7} = 196 \times \frac{4}{7} = 28 \times 4 = 112$ cars.
• State B: Ratio is 5 : 9. Total parts in ratio = $5 + 9 = 14$. The fraction of petrol cars is $\frac{9}{14}$.
  Petrol cars in State B = Total cars in B $\times \frac{9}{14} = 392 \times \frac{9}{14} = 28 \times 9 = 252$ cars.
• State C: Ratio is 5 : 3. Total parts in ratio = $5 + 3 = 8$. The fraction of petrol cars is $\frac{3}{8}$.
  Petrol cars in State C = Total cars in C $\times \frac{3}{8} = 448 \times \frac{3}{8} = 56 \times 3 = 168$ cars.
• State D: Ratio is 1 : 1. Total parts in ratio = $1 + 1 = 2$. The fraction of petrol cars is $\frac{1}{2}$.
  Petrol cars in State D = Total cars in D $\times \frac{1}{2} = 364 \times \frac{1}{2} = 182$ cars.

3. Calculate Total Petrol Cars Across All States

The sum of petrol engine cars in all the states together is the sum of petrol cars calculated for each state.

Total Petrol Cars = (Petrol cars in A) + (Petrol cars in B) + (Petrol cars in C) + (Petrol cars in D)

Total Petrol Cars = $112 + 252 + 168 + 182$

Total Petrol Cars = $364 + 168 + 182 = 532 + 182 = 714$ cars.

Summary Table of Car Distribution and Petrol Cars

The sum of petrol engine cars in all the states together is 714.

Revision Table: Key Calculations

Additional Information: Understanding Ratios and Percentages

This problem combines the concepts of percentages and ratios, commonly used in data interpretation questions.

• Percentages: A percentage represents a part out of a hundred. To find a percentage of a total number, you multiply the total by the percentage divided by 100. For example, 14% of 1400 is $1400 \times \frac{14}{100}$.
• Ratios: A ratio shows the relative size of two or more values. For example, a ratio of 3:4 means for every 3 diesel cars, there are 4 petrol cars. The total number of parts in this ratio is $3 + 4 = 7$. If you know the total number of cars and the ratio, you can find the number of cars for each part of the ratio. The number of petrol cars would be the total cars multiplied by $\frac{\text{Petrol part}}{\text{Total parts}}$.
• In data interpretation, it is crucial to carefully read the question and the table headers to understand what data is being presented and what calculation is required. Break down complex problems into smaller, manageable steps like calculating state totals first, then applying ratios.