Analyzing Company Production and Profit Details

This problem requires us to calculate the cost of production for specific items by different companies based on the total production cost and company-wise breakdowns provided in the table.

The total cost of production for both items together by all seven companies is given as Rs. 25 crores. We need to find the cost of production of item I by company F and the cost of production of item II by company D and then express the former as a percentage of the latter.

Understanding the Provided Data Table

The table gives us the following key pieces of information for each company (A-G):

• Percentage of Total Production: This is the percentage of the overall Rs. 25 crores production cost attributed to that specific company's total production (Items I + II).
• Ratio of production between Items I and II: This ratio tells us how the company's total production cost is split between Item I and Item II.
• Percent (%) Profit Earned: This information about profit is not required to answer this specific question, which is only about production costs.

Calculating Production Cost for Company F, Item I

The total production cost for all companies is Rs. 25 crores.

Company F accounts for 5% of the total production.

Total production cost of company F = $5\%$ of Rs. $25$ crores

Total production cost of company F = $\frac{5}{100} \times 25 = \frac{1}{20} \times 25 = \frac{25}{20} = 1.25$ crores.

Company F's production is divided between Item I and Item II in the ratio 1 : 4.

This means for every $1$ unit of Item I, there are $4$ units of Item II production cost.

The total ratio parts are $1 + 4 = 5$.

The cost of production of Item I by company F is the fraction $\frac{1}{5}$ of company F's total production cost.

Cost of production of Item I by company F = $\frac{1}{5} \times 1.25$ crores

Cost of production of Item I by company F = $0.25$ crores.

Calculating Production Cost for Company D, Item II

Company D accounts for 8% of the total production.

Total production cost of company D = $8\%$ of Rs. $25$ crores

Total production cost of company D = $\frac{8}{100} \times 25 = \frac{2}{25} \times 25 = 2$ crores.

Company D's production is divided between Item I and Item II in the ratio 3 : 5.

This means for every $3$ units of Item I, there are $5$ units of Item II production cost.

The total ratio parts are $3 + 5 = 8$.

The cost of production of Item II by company D is the fraction $\frac{5}{8}$ of company D's total production cost.

Cost of production of Item II by company D = $\frac{5}{8} \times 2$ crores

Cost of production of Item II by company D = $\frac{10}{8} = \frac{5}{4} = 1.25$ crores.

Calculating the Required Percentage

We need to find what percent the cost of production of item I by company F is of the cost of production of item II by company D.

Required Percentage = $\left( \frac{\text{Cost of production of Item I by F}}{\text{Cost of production of Item II by D}} \right) \times 100\%$

Required Percentage = $\left( \frac{0.25 \text{ crores}}{1.25 \text{ crores}} \right) \times 100\%$

Required Percentage = $\left( \frac{0.25}{1.25} \right) \times 100\%$

To simplify the fraction $\frac{0.25}{1.25}$, we can multiply the numerator and denominator by 100 to remove decimals:

$\frac{0.25 \times 100}{1.25 \times 100} = \frac{25}{125}$

Now, simplify the fraction $\frac{25}{125}$: Divide both numerator and denominator by 25.

$\frac{25 \div 25}{125 \div 25} = \frac{1}{5}$

So, the required percentage is $\left( \frac{1}{5} \right) \times 100\%$

Required Percentage = $20\%$.

Step-by-Step Solution Summary

1. Identify the total production cost (Rs. 25 crores).
2. Calculate company F's total production cost based on its percentage of total production.
3. Use the ratio for company F (1:4) to find the cost of production for Item I by F.
4. Calculate company D's total production cost based on its percentage of total production.
5. Use the ratio for company D (3:5) to find the cost of production for Item II by D.
6. Divide the cost of Item I by F by the cost of Item II by D and multiply by 100% to get the final percentage.

Revision Table: Key Calculations

Additional Information: Data Interpretation in Business

Understanding how to interpret data presented in tables and charts is crucial, especially in business and economics. Questions like this one test your ability to:

• Extract relevant numerical data.
• Perform calculations involving percentages and ratios.
• Break down total values into component parts based on given proportions.
• Calculate percentages to compare different values.

This type of data analysis is fundamental for evaluating company performance, market share, cost structures, and profitability. Practice with different data sets helps build proficiency in quick and accurate calculations.