Data Interpretation: Calculating Company Profits from Table

The question asks us to calculate the sum of the profit earned by Company 'B' on the production of item I and the profit earned by Company 'A' on the production of item II, based on the provided table data.

The total cost of production for all seven companies combined is given as Rs. 50 crores. This is the base value upon which percentage costs for individual companies are calculated.

Understanding the Table Data

Let's look at the key columns from the table needed for this calculation:

Total production cost = Rs. 50 crores = Rs. 5000 lakhs (since 1 crore = 100 lakhs).

Step-by-Step Calculation for Company 'B' (Profit on Item I)

First, we calculate the total production cost for Company 'B'.

• Company 'B' accounts for 11% of the total production cost.
• Total cost for Company 'B' = 11% of Rs. 50 crores.
• Cost for B = \( \frac{11}{100} \times 50 \text{ crores} = 0.11 \times 50 = 5.5 \text{ crores} \).
• Cost for B in lakhs = \( 5.5 \times 100 = 550 \text{ lakhs} \).

Next, we find the production cost of Item I for Company 'B'.

• The ratio of production cost for Item I : Item II for Company 'B' is 3 : 2.
• The sum of the ratio parts is \( 3 + 2 = 5 \).
• The cost of Item I for Company 'B' is \( \frac{3}{5} \) of the total cost for Company 'B'.
• Cost of Item I (B) = \( \frac{3}{5} \times 550 \text{ lakhs} = 3 \times 110 = 330 \text{ lakhs} \).

Finally, we calculate the profit earned by Company 'B' on Item I.

• The percentage profit earned by Company 'B' on Item I is 32%.
• Profit on Item I (B) = 32% of the cost of Item I (B).
• Profit on Item I (B) = \( \frac{32}{100} \times 330 \text{ lakhs} = 0.32 \times 330 = 105.6 \text{ lakhs} \).

Step-by-Step Calculation for Company 'A' (Profit on Item II)

First, we calculate the total production cost for Company 'A'.

• Company 'A' accounts for 15% of the total production cost.
• Total cost for Company 'A' = 15% of Rs. 50 crores.
• Cost for A = \( \frac{15}{100} \times 50 \text{ crores} = 0.15 \times 50 = 7.5 \text{ crores} \).
• Cost for A in lakhs = \( 7.5 \times 100 = 750 \text{ lakhs} \).

Next, we find the production cost of Item II for Company 'A'.

• The ratio of production cost for Item I : Item II for Company 'A' is 2 : 3.
• The sum of the ratio parts is \( 2 + 3 = 5 \).
• The cost of Item II for Company 'A' is \( \frac{3}{5} \) of the total cost for Company 'A'.
• Cost of Item II (A) = \( \frac{3}{5} \times 750 \text{ lakhs} = 3 \times 150 = 450 \text{ lakhs} \).

Finally, we calculate the profit earned by Company 'A' on Item II.

• The percentage profit earned by Company 'A' on Item II is 20%.
• Profit on Item II (A) = 20% of the cost of Item II (A).
• Profit on Item II (A) = \( \frac{20}{100} \times 450 \text{ lakhs} = 0.20 \times 450 = 90 \text{ lakhs} \).

Calculating the Sum Total of Profits

The question asks for the sum total of the profit earned by Company 'B' on Item I and the profit earned by Company 'A' on Item II.

• Sum of profits = Profit on Item I (B) + Profit on Item II (A)
• Sum of profits = \( 105.6 \text{ lakhs} + 90 \text{ lakhs} = 195.6 \text{ lakhs} \).

Now, we convert the sum back to crores.

• Sum of profits in crores = \( \frac{195.6}{100} \text{ crores} = 1.956 \text{ crores} \).

Therefore, the sum total of the profit earned by Company 'B' on the production of item I and the profit earned by Company 'A' on the production of item II is Rs. 1.956 crores or Rs. 195.6 lakhs.

Revision Table: Key Values Calculated

Sum of profits (B on I + A on II) = Rs. 105.6 lakhs + Rs. 90 lakhs = Rs. 195.6 lakhs = Rs. 1.956 crores.

Additional Information: Data Interpretation Tips

When tackling data interpretation questions involving tables, it's helpful to follow a structured approach:

• Read the Question Carefully: Understand exactly what is being asked. Identify the specific companies, items, and values required.
• Understand the Table Structure: Look at the headings and the relationship between different columns. Note any total values or base figures given outside the table.
• Identify Relevant Data: Pinpoint the specific rows and columns in the table that contain the information needed for your calculation. Ignore irrelevant data to avoid confusion.
• Break Down the Problem: For multi-step problems like this one, break it down into smaller, manageable calculations. Calculate intermediate values one step at a time.
• Pay Attention to Units: Be consistent with units (crores vs. lakhs) or convert them all to a single unit before performing calculations. Convert back to the required unit for the final answer.
• Use Ratios and Percentages Correctly: Remember how to apply percentage calculations and how to divide a total based on a given ratio.
• Double-Check Calculations: Simple arithmetic errors are common. Quickly review your steps, especially for percentage and ratio calculations.
• Compare with Options: Once you have a result, compare it with the given options. Sometimes options are presented in different units (lakhs vs. crores), so be prepared to convert.

Mastering data interpretation requires practice with various types of tables and charts. Each question provides an opportunity to refine your calculation and analytical skills.