Analyzing Company Production Costs and Ratios

The problem asks us to calculate the cost of production of Item I by company 'F' as a percentage of the cost of production of item II by company 'D'. We are given a table containing data on seven companies (A-G), including the percentage distribution of total production cost, the ratio of production cost between Item I and Item II for each company, and profit percentages (which are not needed for this specific question). The total cost of production for all seven companies combined is Rs. 50 crores.

Understanding the Provided Data Table

Here is the data table:

The first column represents the percentage of the total Rs. 50 crores cost attributable to each company. The second column gives the ratio in which that company's total cost is split between Item I and Item II.

Step-by-Step Calculation

1. Calculate the Total Production Cost for Company F and Company D

The total production cost for all companies is Rs. 50 crores.

• For Company F, the percentage cost is 5%.
  Total cost for Company F = \(5\% \text{ of } 50 \text{ crores} = \frac{5}{100} \times 50 = \frac{1}{20} \times 50 = 2.5\) crores.
• For Company D, the percentage cost is 8%.
  Total cost for Company D = \(8\% \text{ of } 50 \text{ crores} = \frac{8}{100} \times 50 = \frac{2}{25} \times 50 = 4\) crores.

2. Calculate the Cost of Item I for Company F

Company F's total cost (Rs. 2.5 crores) is distributed between Item I and Item II in the ratio 1:4. The sum of the ratio parts is \(1 + 4 = 5\).

The fraction of the cost for Item I is \(\frac{1}{5}\).

Cost of production of Item I by Company F = \(\frac{1}{5} \times \text{Total cost for F} = \frac{1}{5} \times 2.5 = \frac{1}{5} \times \frac{5}{2} = \frac{1}{2} = 0.5\) crores.

3. Calculate the Cost of Item II for Company D

Company D's total cost (Rs. 4 crores) is distributed between Item I and Item II in the ratio 3:5. The sum of the ratio parts is \(3 + 5 = 8\).

The fraction of the cost for Item II is \(\frac{5}{8}\).

Cost of production of Item II by Company D = \(\frac{5}{8} \times \text{Total cost for D} = \frac{5}{8} \times 4 = \frac{20}{8} = \frac{5}{2} = 2.5\) crores.

4. Calculate the Percentage

We need to find what percentage the cost of production of item I by company 'F' (Rs. 0.5 crores) is of the cost of production of item II by company 'D' (Rs. 2.5 crores).

Percentage = \(\frac{\text{Cost of Item I by F}}{\text{Cost of Item II by D}} \times 100\) Percentage = \(\frac{0.5}{2.5} \times 100\) Percentage = \(\frac{\frac{1}{2}}{\frac{5}{2}} \times 100\) Percentage = \(\frac{1}{2} \times \frac{2}{5} \times 100\) Percentage = \(\frac{1}{5} \times 100\) Percentage = \(20\%\)

Thus, the cost of production of item I by company 'F' is 20% of the cost of production of item II by company 'D'.

Revision Table: Key Calculations

Percentage Calculation: \(\frac{\text{Cost of Item I by F}}{\text{Cost of Item II by D}} \times 100 = \frac{0.5}{2.5} \times 100 = 0.2 \times 100 = 20\%\)

Additional Information on Data Interpretation

Data Interpretation questions often require careful reading of the table headers and footnotes. In this problem, understanding what the percentages in the first column refer to (percentage of the total cost across all companies) and how the ratios in the second column work (splitting the cost *within* that company) is crucial.

• Percentage Distribution: When a percentage distribution is given, it usually means each part is a percentage of the total value provided (here, Rs. 50 crores).
• Ratios: A ratio like a:b means the quantity is divided into \(a+b\) parts, with the first quantity taking \(a\) parts and the second taking \(b\) parts.
• Profit Calculation: While not used here, profit is typically calculated on the cost price. Profit % = \(\frac{\text{Profit}}{\text{Cost}} \times 100\), which means Profit = \(\frac{\text{Profit \%}}{100} \times \text{Cost}\). Selling Price = Cost + Profit.

Practice with different types of tables and charts (bar graphs, pie charts, line graphs) helps improve data interpretation skills for competitive exams.