Calculating Company D's Profit on Item II Production

This problem requires us to analyze the provided table data to determine the profit earned by Company 'D' specifically on Item II. We are given the total production cost for all seven companies combined and specific details for each company regarding their cost distribution, ratio of production costs for two items, and profit percentages.

Understanding the Given Data

• Total production cost for all seven companies (A-G) is Rs. 50 crores.
• The table provides:
  • The percentage share of the total Rs. 50 crores production cost for each company.
  • The ratio of the production cost between Item I and Item II for each company.
  • The percentage profit earned on Item I and Item II for each company.

Step-by-Step Calculation for Company D's Profit on Item II

We need to find the amount of profit earned by Company 'D' on Item II. To do this, we will follow these steps:

Step 1: Calculate the total production cost for Company D.

From the table, the percentage cost distribution for Company D is 8% of the total cost for all companies. The total cost for all companies is Rs. 50 crores.

Total cost for Company D = \( 8\% \text{ of } Rs. 50 \text{ crores} \)

Total cost for Company D = \( \frac{8}{100} \times 50 \text{ crores} \)

Total cost for Company D = \( 0.08 \times 50 \text{ crores} \)

Total cost for Company D = \( Rs. 4 \text{ crores} \)

Step 2: Calculate the production cost of Item II for Company D.

The ratio of production cost for Item I to Item II for Company D is given as 15:25. This means for every 15 units of cost for Item I, there are 25 units of cost for Item II. The total ratio parts are \(15 + 25 = 40\).

The cost of Item II is \( \frac{25}{40} \) of the total cost for Company D.

Cost of Item II for Company D = \( \frac{25}{40} \times \text{Total cost for Company D} \)

Cost of Item II for Company D = \( \frac{25}{40} \times Rs. 4 \text{ crores} \)

We can simplify the fraction \( \frac{25}{40} \) by dividing both numerator and denominator by 5: \( \frac{5}{8} \).

Cost of Item II for Company D = \( \frac{5}{8} \times Rs. 4 \text{ crores} \)

Cost of Item II for Company D = \( \frac{5 \times 4}{8} \text{ crores} = \frac{20}{8} \text{ crores} = \frac{5}{2} \text{ crores} \)

Cost of Item II for Company D = \( Rs. 2.5 \text{ crores} \)

Step 3: Calculate the profit earned on Item II by Company D.

From the table, the percentage profit earned by Company D on Item II is 25%.

Profit on Item II for Company D = \( 25\% \text{ of Cost of Item II for Company D} \)

Profit on Item II for Company D = \( \frac{25}{100} \times Rs. 2.5 \text{ crores} \)

Profit on Item II for Company D = \( 0.25 \times 2.5 \text{ crores} \)

Profit on Item II for Company D = \( Rs. 0.625 \text{ crores} \)

Step 4: Convert the profit amount to lakhs.

We know that 1 crore = 100 lakhs.

Profit on Item II for Company D in lakhs = \( Rs. 0.625 \times 100 \text{ lakhs} \)

Profit on Item II for Company D = \( Rs. 62.5 \text{ lakhs} \)

Based on our calculation, the amount of profit earned by Company 'D' on Item II is Rs. 62.5 lakhs.

Summary of Results for Company D

• Total Production Cost: Rs. 4 crores
• Production Cost of Item II: Rs. 2.5 crores
• Profit Percentage on Item II: 25%
• Amount of Profit on Item II: Rs. 62.5 lakhs

Comparing this result with the given options, we find that Option 4 matches our calculated profit.

Revision Table: Key Calculations for Company D Profit

Additional Information: Data Interpretation Skills

Data interpretation questions, especially those involving tables, require careful reading and understanding of what each column and row represents. It's crucial to identify the base value (here, the total Rs. 50 crores) and how the percentages and ratios relate to it. Breaking down the problem into smaller steps, such as calculating the company's total cost first, then item-specific costs, and finally profits, helps avoid errors. Pay close attention to units (crores vs. lakhs) when providing the final answer.