Understanding Bicycle Production and Profit Data

The question asks us to find the difference in profit earned by two different companies on two different bicycle models, based on the provided table which contains distribution of production, production ratios, and profit percentages.

The total production cost for all six companies combined is given as Rs. 6.4 crore.

First, let's look at the relevant data for Company C and Company E from the table:

Step 1: Calculate the Total Production Cost for Company C and Company E

The total production cost for all companies is Rs. 6.4 crore.

• Production distribution for Company C is 22%.
• Production distribution for Company E is 10%.

So, the total production cost for Company C is:

\( \text{Cost for C} = 22\% \text{ of } 6.4 \text{ crore} \)

\( \text{Cost for C} = \frac{22}{100} \times 6.4 = 0.22 \times 6.4 = 1.408 \text{ crore} \)

The total production cost for Company E is:

\( \text{Cost for E} = 10\% \text{ of } 6.4 \text{ crore} \)

\( \text{Cost for E} = \frac{10}{100} \times 6.4 = 0.10 \times 6.4 = 0.64 \text{ crore} \)

Step 2: Calculate the Production Cost of Model L for Company C

For Company C, the production ratio of Model L to Model M (L:M) is 6:5.

The total ratio parts are \(6 + 5 = 11\).

The production cost of Model L for Company C is:

\( \text{Cost of Model L for C} = \left( \frac{\text{Ratio of L}}{\text{Total Ratio Parts}} \right) \times \text{Total Cost for C} \)

\( \text{Cost of Model L for C} = \left( \frac{6}{11} \right) \times 1.408 \)

\( \text{Cost of Model L for C} = 6 \times \frac{1.408}{11} = 6 \times 0.128 = 0.768 \text{ crore} \)

Step 3: Calculate the Profit Earned by Company C on Model L

The profit percentage for Model L for Company C is 20%.

The profit earned on Model L by Company C is:

\( \text{Profit on Model L for C} = 20\% \text{ of Cost of Model L for C} \)

\( \text{Profit on Model L for C} = \frac{20}{100} \times 0.768 = 0.20 \times 0.768 = 0.1536 \text{ crore} \)

Step 4: Calculate the Production Cost of Model M for Company E

For Company E, the production ratio of Model L to Model M (L:M) is 2:3.

The total ratio parts are \(2 + 3 = 5\).

The production cost of Model M for Company E is:

\( \text{Cost of Model M for E} = \left( \frac{\text{Ratio of M}}{\text{Total Ratio Parts}} \right) \times \text{Total Cost for E} \)

\( \text{Cost of Model M for E} = \left( \frac{3}{5} \right) \times 0.64 \)

\( \text{Cost of Model M for E} = 0.6 \times 0.64 = 0.384 \text{ crore} \)

Step 5: Calculate the Profit Earned by Company E on Model M

The profit percentage for Model M for Company E is 21%.

The profit earned on Model M by Company E is:

\( \text{Profit on Model M for E} = 21\% \text{ of Cost of Model M for E} \)

\( \text{Profit on Model M for E} = \frac{21}{100} \times 0.384 = 0.21 \times 0.384 = 0.08064 \text{ crore} \)

Step 6: Calculate the Difference in Profits

We need to find the difference between the profit earned by Company C on model L and the profit earned by Company E on model M.

\( \text{Difference} = \text{Profit on Model L for C} - \text{Profit on Model M for E} \)

\( \text{Difference} = 0.1536 - 0.08064 \)

\( \text{Difference} = 0.07296 \text{ crore} \)

The difference between the profit earned by Company C on model L and by Company E on model M is 0.07296 crore.

Revision Table: Key Calculations Summary

Additional Information on Profit Calculation

In business, profit is often calculated as a percentage of cost or a percentage of revenue. In this problem, the profit percentages are applied to the production cost of each model.

• Production Cost: The cost incurred by the company to manufacture a product.
• Profit Percentage: The profit expressed as a percentage of the cost (or sometimes revenue). A 20% profit on cost means the profit is 20% of the production cost.
• Total Profit: The sum of profit earned from all units sold. In this case, the profit is calculated based on the total cost allocated to the production of each model for a company.

Understanding how to break down total costs based on ratios and then apply profit percentages is crucial for solving such data interpretation problems.