Analyzing Car Distribution Across States

The problem provides a table showing the percentage distribution of a total of 1400 cars across four states (A, B, C, D) and the ratio of diesel engine cars to petrol engine cars within each state.

We need to find out what percentage more the number of petrol engine cars in State 'C' is compared to the number of diesel engine cars in State 'A'.

Understanding the Data Table

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

Calculating Cars in State C

First, let's calculate the total number of cars in State C.

• Total number of cars = 1400
• Percentage of cars in State C = 32%
• Number of cars in State C = \(1400 \times \frac{32}{100}\)
• Number of cars in State C = \(14 \times 32 = 448\)

Next, we need to find the number of petrol engine cars in State C. The ratio of Diesel : Petrol cars in State C is 5 : 3.

• Ratio parts = 5 + 3 = 8
• Petrol cars represent 3 parts out of 8.
• Number of petrol engine cars in State C = \(448 \times \frac{3}{8}\)
• Number of petrol engine cars in State C = \(56 \times 3 = 168\)

So, there are 168 petrol engine cars in State C.

Calculating Cars in State A

Now, let's calculate the total number of cars in State A.

• Total number of cars = 1400
• Percentage of cars in State A = 14%
• Number of cars in State A = \(1400 \times \frac{14}{100}\)
• Number of cars in State A = \(14 \times 14 = 196\)

Next, we need to find the number of diesel engine cars in State A. The ratio of Diesel : Petrol cars in State A is 3 : 4.

• Ratio parts = 3 + 4 = 7
• Diesel cars represent 3 parts out of 7.
• Number of diesel engine cars in State A = \(196 \times \frac{3}{7}\)
• Number of diesel engine cars in State A = \(28 \times 3 = 84\)

So, there are 84 diesel engine cars in State A.

Finding the Percentage Difference

We need to find what percent more the number of petrol engine cars in State C (168) is than the number of diesel engine cars in State A (84).

The difference is \(168 - 84 = 84\).

To find the percentage more, we use the formula:

\(\text{Percentage More} = \frac{\text{(Value 1 - Value 2)}}{\text{Value 2}} \times 100\%\)

Here, Value 1 is the number of petrol cars in C (168) and Value 2 is the number of diesel cars in A (84).

\(\text{Percentage More} = \frac{(168 - 84)}{84} \times 100\%\)

\(\text{Percentage More} = \frac{84}{84} \times 100\%\)

\(\text{Percentage More} = 1 \times 100\% = 100\%\)

Thus, the number of petrol engine cars in State 'C' is 100% more than the number of diesel engine cars in State 'A'.

Revision Table: Key Calculations

Additional Information: Percentage Calculations

Understanding percentage calculations is crucial for data interpretation questions. When asked "what percent more than Y is X?", the formula is \(\frac{(X - Y)}{Y} \times 100\%\). When asked "what percent of Y is X?", the formula is \(\frac{X}{Y} \times 100\%\). In this problem, we used the 'percentage more' formula because we wanted to know the increase relative to the base value (diesel cars in State A).

Ratio problems involve dividing a total quantity according to given parts. If a quantity is divided in the ratio a : b, the total parts are a + b. The first part is \(\frac{a}{(a+b)}\) of the total, and the second part is \(\frac{b}{(a+b)}\) of the total.