Understanding the Production and Profit Data

The problem provides data about the production and profit of two items, Item I and Item II, across seven different companies (A to G). The total cost of production for both items combined across all seven companies is given as Rs. 25 crores. We are asked to find the sum of the profit earned by company B specifically on the production of Item I and the profit earned by company A specifically on the production of Item II.

Total Production Cost Conversion

The total production cost is given in crores, but the options are in Lakhs. Let's convert the total production cost to Lakhs for easier calculation and comparison with the options.

Total Production Cost = Rs. $25$ crores

Since $1$ crore = $100$ Lakhs,

Total Production Cost = Rs. $25 \times 100$ Lakhs = Rs. $2500$ Lakhs.

Step-by-Step Profit Calculation for Company A and Company B

We need to calculate the profit for specific items from specific companies. This involves several steps:

1. Determine the total production cost for the specific company based on its percentage of the total production.
2. Distribute the company's production cost between Item I and Item II based on the given ratio.
3. Calculate the profit for the specific item using the item's profit percentage and its production cost.

Calculations for Company A (Profit on Item II)

• Percentage of Total Production for Company A = $15\%$
• Total Production Cost for Company A = $15\%$ of Total Production Cost
• Total Production Cost for Company A = $\frac{15}{100} \times 2500$ Lakhs
• Total Production Cost for Company A = $0.15 \times 2500$ Lakhs = $375$ Lakhs.

• Ratio of production between Item I and Item II for Company A = $2 : 3$
• This means that for every $2$ units of Item I, $3$ units of Item II are produced (in terms of cost distribution). The total ratio parts are $2 + 3 = 5$.
• Production cost of Item II by Company A = $\frac{3}{(2+3)} \times \text{Total Production Cost for Company A}$
• Production cost of Item II by Company A = $\frac{3}{5} \times 375$ Lakhs
• Production cost of Item II by Company A = $3 \times \frac{375}{5}$ Lakhs = $3 \times 75$ Lakhs = $225$ Lakhs.

• Percent Profit Earned for Item II by Company A = $20\%$
• Profit earned by Company A on production of Item II = $20\%$ of Production cost of Item II by Company A
• Profit earned by Company A on production of Item II = $\frac{20}{100} \times 225$ Lakhs
• Profit earned by Company A on production of Item II = $0.20 \times 225$ Lakhs = $45$ Lakhs.

Calculations for Company B (Profit on Item I)

• Percentage of Total Production for Company B = $11\%$
• Total Production Cost for Company B = $11\%$ of Total Production Cost
• Total Production Cost for Company B = $\frac{11}{100} \times 2500$ Lakhs
• Total Production Cost for Company B = $0.11 \times 2500$ Lakhs = $275$ Lakhs.

• Ratio of production between Item I and Item II for Company B = $3 : 2$
• This means the total ratio parts are $3 + 2 = 5$.
• Production cost of Item I by Company B = $\frac{3}{(3+2)} \times \text{Total Production Cost for Company B}$
• Production cost of Item I by Company B = $\frac{3}{5} \times 275$ Lakhs
• Production cost of Item I by Company B = $3 \times \frac{275}{5}$ Lakhs = $3 \times 55$ Lakhs = $165$ Lakhs.

• Percent Profit Earned for Item I by Company B = $32\%$
• Profit earned by Company B on production of Item I = $32\%$ of Production cost of Item I by Company B
• Profit earned by Company B on production of Item I = $\frac{32}{100} \times 165$ Lakhs
• Profit earned by Company B on production of Item I = $0.32 \times 165$ Lakhs.
• Calculation: $0.32 \times 165 = \frac{32}{100} \times 165 = \frac{8}{25} \times 165 = 8 \times 6.6 = 52.8$ Lakhs.

Sum Total of Profits

We need to find the sum total of the profit earned by company B on production of item I and the profit earned by company A on the production of item II.

Sum Total = Profit (Company B, Item I) + Profit (Company A, Item II)

Sum Total = $52.8$ Lakhs + $45$ Lakhs

Sum Total = $97.8$ Lakhs.

The sum total of the profits is Rs. $97.8$ Lakhs.

Let's summarize the calculated profits in a table:

Sum of Profits = $45 + 52.8 = 97.8$ Lakhs.

Conclusion

Based on the calculations, the sum total of the profit earned by company B on production of item I and the profit earned by company A on the production of item II is Rs. $97.8$ Lakhs.

Revision Table: Production and Profit Calculation Summary

Sum = $45 + 52.8 = 97.8$ Lakhs.

Additional Information: Data Interpretation Concepts

This problem is an example of data interpretation, where information is presented in tables or charts, and specific questions need to be answered by analyzing the data. Key concepts used here include:

• Percentages: Used to determine a part of a whole. For example, the percentage of total production for each company.
• Ratios: Used to show the relative proportion of two or more quantities. Here, the ratio of production cost between Item I and Item II for each company.
• Profit Calculation: Profit is typically calculated as a percentage of the cost price (in this case, production cost) or selling price. Here, it's a percentage of the production cost.
• Unit Conversion: Converting between different units like crores and lakhs is crucial for consistency in calculations and matching option formats.

Solving such problems requires careful reading of the question, accurate extraction of relevant data from the table, and applying the correct mathematical operations (percentage calculation, ratio division, multiplication, and addition).