Let's analyze the given data table step-by-step to find the difference between the total number of products P and Q produced by company F.

Understanding the Data for Company F

The table provides several pieces of information for each company, including company F. We need to extract the relevant data points for company F to solve this particular problem.

• Total number of products P and Q produced by all six companies is 8 lakhs (which is 800,000).
• The percentage distribution of total products (P and Q combined) produced by company F is 8%.
• The ratio of products P to products Q produced by company F is 3:2.

Calculating Total Products by Company F

First, we need to find the total number of products (P + Q) produced specifically by company F. This is given as 8% of the total products produced by all companies.

Total products by all companies = 800,000

Percentage of products by Company F = 8%

Total products produced by Company F = \( 8\% \text{ of } 800,000 \)

\( \text{Total products by F} = \frac{8}{100} \times 800,000 \)

\( \text{Total products by F} = 8 \times 8,000 \)

\( \text{Total products by F} = 64,000 \)

So, company F produced a total of 64,000 products (P and Q combined).

Determining Products P and Q Individually for Company F

Now we know the total number of products produced by company F (64,000) and the ratio of product P to product Q (3:2). We can use this ratio to find the exact number of products P and Q.

Ratio of P to Q for Company F = 3:2

The sum of the ratio parts is \( 3 + 2 = 5 \).

This means that for every 5 products produced by company F, 3 are product P and 2 are product Q.

Number of product P produced by Company F = \( \frac{\text{Ratio part for P}}{\text{Sum of ratio parts}} \times \text{Total products by F} \)

\( \text{Product P by F} = \frac{3}{5} \times 64,000 \)

\( \text{Product P by F} = 3 \times \frac{64,000}{5} \)

\( \text{Product P by F} = 3 \times 12,800 \)

\( \text{Product P by F} = 38,400 \)

Number of product Q produced by Company F = \( \frac{\text{Ratio part for Q}}{\text{Sum of ratio parts}} \times \text{Total products by F} \)

\( \text{Product Q by F} = \frac{2}{5} \times 64,000 \)

\( \text{Product Q by F} = 2 \times \frac{64,000}{5} \)

\( \text{Product Q by F} = 2 \times 12,800 \)

\( \text{Product Q by F} = 25,600 \)

We can quickly check if these numbers add up to the total: \( 38,400 + 25,600 = 64,000 \), which is correct.

Calculating the Difference Between Products P and Q by Company F

The question asks for the difference between the total number of products P and Q produced by company F.

Difference = Number of Product P by F - Number of Product Q by F

\( \text{Difference} = 38,400 - 25,600 \)

\( \text{Difference} = 12,800 \)

The difference between the total number of products P and Q produced by company F is 12,800.

Summary of Calculations for Company F

Here is a quick summary of the values calculated for company F:

Conclusion

Based on the calculations, the difference between the total number of products P and Q produced by company F is 12,800.

Revision Table: Products by Company F

Reviewing the key steps and values for company F:

• Total overall production: 8,00,000
• F's share of production: 8%
• Total production by F: 64,000
• F's P:Q ratio: 3:2
• F's P production: 38,400
• F's Q production: 25,600
• Difference (P-Q): 12,800

Additional Information: Data Interpretation Skills

Solving this type of data interpretation problem requires carefully reading the question and extracting the relevant information from the table. It involves calculations based on percentages and ratios. Key steps often include:

• Understanding the total base value (e.g., total production across all companies).
• Calculating the specific value for the company or category mentioned (e.g., total production by company F).
• Using ratios or other percentages provided to break down the specific value into required components (e.g., splitting F's total production into P and Q).
• Performing the final calculation requested (e.g., finding the difference).

Practice with different types of data interpretation questions helps improve speed and accuracy in exams.