Analyzing Product Distribution and Sales Data

The question asks us to find the number of products P sold by company A as a percentage of the number of products P sold by company F. To do this, we need to extract information from the provided table and perform calculations step-by-step.

The total number of products P and Q produced by all six companies combined is given as 8 lakhs, which is equal to 8,00,000.

Calculating Products P Sold by Company A

First, let's find the total number of products (P + Q) produced by Company A. According to the table, Company A accounts for 24% of the total products.

• Total products in Company A = 24% of 8,00,000
• Total products in Company A = $0.24 \times 8,00,000 = 1,92,000$

Next, we use the ratio of P to Q for Company A, which is 5:3, to find the number of products P produced by Company A.

• Ratio parts for P and Q = 5 + 3 = 8
• Number of products P produced by A = (Ratio of P / Total ratio parts) $\times$ Total products in A
• Number of products P produced by A = $(5/8) \times 1,92,000$
• Number of products P produced by A = $5 \times (1,92,000 / 8) = 5 \times 24,000 = 1,20,000$

Finally, we find the number of products P sold by Company A. The table shows that 65% of products P produced by Company A were sold.

• Number of products P sold by A = 65% of 1,20,000
• Number of products P sold by A = $0.65 \times 1,20,000 = 78,000$

Calculating Products P Sold by Company F

Now, let's perform similar calculations for Company F. According to the table, Company F accounts for 8% of the total products.

• Total products in Company F = 8% of 8,00,000
• Total products in Company F = $0.08 \times 8,00,000 = 64,000$

The ratio of P to Q for Company F is 3:2. We use this to find the number of products P produced by Company F.

• Ratio parts for P and Q = 3 + 2 = 5
• Number of products P produced by F = (Ratio of P / Total ratio parts) $\times$ Total products in F
• Number of products P produced by F = $(3/5) \times 64,000$
• Number of products P produced by F = $3 \times (64,000 / 5) = 3 \times 12,800 = 38,400$

Lastly, we find the number of products P sold by Company F. The table indicates that 50% of products P produced by Company F were sold.

• Number of products P sold by F = 50% of 38,400
• Number of products P sold by F = $0.50 \times 38,400 = 19,200$

Finding the Percentage

The question asks for the number of products P sold by company A as a percentage of the number of products P sold by company F. We have calculated:

• Products P sold by Company A = 78,000
• Products P sold by Company F = 19,200

Percentage = (Number of products P sold by A / Number of products P sold by F) $\times$ 100

Percentage = $(78,000 / 19,200) \times 100$

Percentage = $(780 / 192) \times 100$

Percentage = $(390 / 96) \times 100$

Percentage = $(195 / 48) \times 100$

Percentage = $(65 / 16) \times 100$

Percentage = $4.0625 \times 100$

Percentage = $406.25$

Thus, the number of products P sold by company A is 406.25% of the number of products P sold by company F.

Revision Table: Key Calculations

Final Percentage Calculation: $(78,000 / 19,200) \times 100 = 406.25\%$

Additional Information: Data Interpretation Tips

Data interpretation questions, especially those involving tables and percentages, require careful reading and systematic calculation. Here are some tips:

• Understand the Question: Clearly identify what is being asked. In this case, it's a percentage comparison of sales of a specific product type (P) from two companies (A and F).
• Break Down the Data: The table provides multiple layers of information: total distribution, product ratio, and sales percentage. You need to use these layers sequentially.
• Calculate Base Values First: Start by finding the total quantity relevant to the company (e.g., total products for Company A and F) before calculating specific product types or sales.
• Use Ratios Correctly: Remember that a ratio like 5:3 means the total is 5+3=8 parts, and P represents 5 of those 8 parts.
• Percentage Calculations: Be precise with percentage calculations, whether it's finding a percentage of a number or expressing one number as a percentage of another. Remember that 'X% of Y' is $(X/100) \times Y$, and 'X is what percentage of Y' is $(X/Y) \times 100$.
• Stay Organized: Keep track of the numbers you calculate at each step to avoid errors.

These techniques help ensure accuracy when working with complex data sets like the one presented in the table.