Let's break down this data interpretation problem step by step to find the total profit earned by Company G for both items.

Understanding the Problem

The problem provides a table containing production and profit details for seven different companies (A-G). The total cost of production for all companies combined for both items is Rs. 25 crores. For each company, we are given:

• The percentage of the total production cost they represent.
• The ratio in which they produce Item I and Item II.
• The percentage profit earned on Item I and Item II separately.

We need to calculate the total profit earned by Company G from producing both Item I and Item II.

Analyzing the Data for Company G

First, let's identify the relevant data for Company G from the provided table.

We are given that the total production cost for all seven companies is Rs. 25 crores.

Total Production Cost = Rs. 25 crores = Rs. 25,00,00,000

Step-by-Step Profit Calculation for Company G

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

Company G accounts for 12% of the total production cost.

Total Production Cost of Company G = 12% of Rs. 25,00,00,000

\( \text{Cost}_G = \frac{12}{100} \times 25,00,00,000 \)

\( \text{Cost}_G = 0.12 \times 25,00,00,000 \)

\( \text{Cost}_G = 3,00,00,000 \)

So, the total production cost for Company G is Rs. 3,00,00,000 (or Rs. 3 crores).

Step 2: Distribute the production cost between Item I and Item II for Company G.

The ratio of production between Item I and Item II for Company G is 1 : 2. This means for every 1 unit of cost on Item I, there are 2 units of cost on Item II, making a total of \(1 + 2 = 3\) parts.

Production Cost for Item I (Company G) = \( \frac{\text{Ratio for Item I}}{\text{Sum of ratios}} \times \text{Total Cost of G} \)

\( \text{Cost}_{G, I} = \frac{1}{3} \times 3,00,00,000 \)

\( \text{Cost}_{G, I} = 1,00,00,000 \)

Production Cost for Item II (Company G) = \( \frac{\text{Ratio for Item II}}{\text{Sum of ratios}} \times \text{Total Cost of G} \)

\( \text{Cost}_{G, II} = \frac{2}{3} \times 3,00,00,000 \)

\( \text{Cost}_{G, II} = 2,00,00,000 \)

The production cost for Item I is Rs. 1,00,00,000 and for Item II is Rs. 2,00,00,000.

Step 3: Calculate the profit earned from Item I for Company G.

Company G earns a 30% profit on Item I.

Profit from Item I (Company G) = 30% of Production Cost for Item I

\( \text{Profit}_{G, I} = \frac{30}{100} \times 1,00,00,000 \)

\( \text{Profit}_{G, I} = 0.30 \times 1,00,00,000 \)

\( \text{Profit}_{G, I} = 30,00,000 \)

Step 4: Calculate the profit earned from Item II for Company G.

Company G earns a 24% profit on Item II.

Profit from Item II (Company G) = 24% of Production Cost for Item II

\( \text{Profit}_{G, II} = \frac{24}{100} \times 2,00,00,000 \)

\( \text{Profit}_{G, II} = 0.24 \times 2,00,00,000 \)

\( \text{Profit}_{G, II} = 48,00,000 \)

Step 5: Calculate the total profit earned by Company G for both items.

Total Profit (Company G) = Profit from Item I + Profit from Item II

\( \text{Total Profit}_G = \text{Profit}_{G, I} + \text{Profit}_{G, II} \)

\( \text{Total Profit}_G = 30,00,000 + 48,00,000 \)

\( \text{Total Profit}_G = 78,00,000 \)

The total profit earned by Company G is Rs. 78,00,000.

Converting to Lakhs:

1 Lakh = Rs. 1,00,000

Rs. 78,00,000 = \( \frac{78,00,000}{1,00,000} \) Lakhs = 78 Lakhs.

The total profit earned by Company G is Rs. 78 Lakhs.

Summary of Calculations

• Total production cost of Company G: Rs. 3 crores
• Production cost of Item I by Company G: Rs. 1 crore
• Production cost of Item II by Company G: Rs. 2 crores
• Profit from Item I by Company G: Rs. 30 Lakhs
• Profit from Item II by Company G: Rs. 48 Lakhs
• Total profit by Company G: Rs. 78 Lakhs

Revision Table: Key Concepts for Data Interpretation

Additional Information: Data Interpretation Strategies

Data interpretation questions often require careful reading of the table and question, followed by applying basic mathematical concepts like percentages, ratios, averages, and sometimes charts (like bar graphs or pie charts). Here are some tips:

• Read the title and headings of the table or chart carefully to understand what the data represents.
• Identify the specific information needed to answer the question.
• Pay attention to units (like crores, lakhs, thousands, percentages, ratios).
• Break down the problem into smaller, manageable steps.
• Perform calculations accurately. Double-check your arithmetic.
• Convert units as needed (e.g., crores to lakhs or vice versa) to match the options given in the question.
• Practice with different types of data representation (tables, bar graphs, pie charts, line graphs).

Mastering these concepts and techniques is crucial for success in competitive exams where data interpretation is a common section.