Finding Non-AC Diesel Cars in State C

The question asks us to find the number of non-Air-Conditioned (AC) diesel engine cars in State 'C', based on the provided data table and additional information.

Understanding the Given Data

We are given the total number of cars across four states (A, B, C, D) and the percentage distribution of these cars in each state. We also have the ratio of diesel engine cars to petrol engine cars for each state. Additionally, we are told that 25% of the diesel cars in State 'C' are Air-Conditioned (AC).

Total number of cars in all four states = 1400.

Step-by-Step Calculation

Let's break down the problem into smaller steps to find the required number.

Step 1: Calculate the Total Number of Cars in State 'C'

State 'C' has 32% of the total cars. The total number of cars is 1400.

Number of cars in State 'C' = Total cars $\times$ Percentage distribution in State 'C'

Number of cars in State 'C' = $1400 \times \frac{32}{100}$

Number of cars in State 'C' = $14 \times 32 = 448$

So, there are 448 cars in State 'C'.

Step 2: Calculate the Number of Diesel Engine Cars in State 'C'

In State 'C', the ratio of Diesel engine cars to Petrol engine cars is 5 : 3. This means for every 5 diesel cars, there are 3 petrol cars. The total parts in the ratio are $5 + 3 = 8$.

The number of diesel cars is $\frac{5}{8}$ of the total cars in State 'C'.

Number of diesel cars in State 'C' = Total cars in State 'C' $\times \frac{\text{Diesel Ratio Part}}{\text{Total Ratio Parts}}$

Number of diesel cars in State 'C' = $448 \times \frac{5}{8}$

Number of diesel cars in State 'C' = $56 \times 5 = 280$

So, there are 280 diesel engine cars in State 'C'.

Step 3: Calculate the Number of AC Diesel Cars in State 'C'

We are given that 25% of the diesel engine cars in State 'C' are Air-Conditioned (AC).

Number of AC diesel cars in State 'C' = Total diesel cars in State 'C' $\times$ Percentage of AC diesel cars

Number of AC diesel cars in State 'C' = $280 \times \frac{25}{100}$

Number of AC diesel cars in State 'C' = $280 \times \frac{1}{4} = 70$

So, there are 70 AC diesel engine cars in State 'C'.

Step 4: Calculate the Number of Non-AC Diesel Cars in State 'C'

The total number of diesel cars in State 'C' is 280. These cars are either AC or non-AC. Number of non-AC diesel cars = Total diesel cars - Number of AC diesel cars

Number of non-AC diesel cars in State 'C' = $280 - 70 = 210$

Therefore, there are 210 non-AC diesel engine cars in State 'C'.

Summary of Calculation

• Total cars = 1400
• Cars in State C = 32% of 1400 = 448
• Ratio (Diesel:Petrol) in State C = 5:3 (Total parts = 8)
• Diesel cars in State C = (5/8) of 448 = 280
• AC diesel cars in State C = 25% of 280 = 70
• Non-AC diesel cars in State C = Total diesel cars - AC diesel cars = 280 - 70 = 210

The number of diesel engine cars which are non-AC in State 'C' is 210.

Revision Table: Key Calculations for State C Cars

Additional Information: Understanding Data Analysis

This problem involves interpreting data presented in a table and performing calculations based on percentages and ratios. Here are some related concepts:

• Percentage: A percentage represents a part out of one hundred. For example, 32% means 32 out of every 100. To find a percentage of a number, convert the percentage to a decimal or fraction and multiply by the number.
• Ratio: A ratio compares two or more quantities. A ratio of 5:3 means that for every 5 units of the first quantity, there are 3 units of the second quantity. The total number of parts in the ratio is the sum of the ratio terms (5+3=8). To find the value of one part, divide the total amount by the total number of parts.
• Data Interpretation: Reading data from tables, charts, or graphs requires careful attention to headings, labels, and values. Understanding what each column or row represents is crucial for accurate calculations.
• Problem Solving Steps: Complex problems can be solved by breaking them down into smaller, manageable steps. First, identify what is given and what needs to be found. Then, determine the calculations needed at each step using the relevant data.