Understanding the Bicycle Production Profit Problem

The question asks us to calculate the combined profit earned on Model M bicycles by Companies B and C. We are given a table containing information about the percentage distribution of total production, the ratio of production of two models (L and M), and the profit percentages for each model, across six different companies (A-F). The total production cost for all six companies is also provided as Rs. 6.4 crore.

To solve this, we need to follow these steps:

1. Determine the total production cost for Company B and Company C based on their percentage distribution of the overall production cost. We assume the production cost distribution is proportional to the percentage distribution of production.
2. For each company (B and C), use the production ratio of Model L to Model M to find the proportion of their total production cost attributable to Model M.
3. Calculate the actual production cost for Model M for each company.
4. Use the given profit percentage for Model M to calculate the profit earned on Model M for each company.
5. Add the profits on Model M for Company B and Company C to get the total combined profit.

Analyzing the Data Table

Let's look at the relevant data for Companies B and C from the provided table.

Total Production Cost for all companies = Rs. 6.4 crore.

Step-by-Step Profit Calculation

Calculating Production Cost for Companies B and C

The total production cost for all six companies is Rs. 6.4 crore. The cost for each company is proportional to its percentage distribution of production.

• Production cost for Company B = 14% of Rs. 6.4 crore
• Production cost for Company C = 22% of Rs. 6.4 crore

Calculation:

• Production cost for Company B = \(0.14 \times 6.4 \text{ crore}\) = \(0.896 \text{ crore}\)
• Production cost for Company C = \(0.22 \times 6.4 \text{ crore}\) = \(1.408 \text{ crore}\)

Calculating Production Cost for Model M for Companies B and C

For each company, the total production cost is split between Model L and Model M based on their production ratio. We assume the cost split is in the same ratio as the production volume ratio.

For Company B:

• Production Ratio L:M is 9:5.
• Total parts in ratio = \(9 + 5 = 14\).
• The fraction of cost for Model M is \(\frac{5}{14}\).
• Cost of Model M production for Company B = \(\frac{5}{14} \times \text{Total production cost of B}\)
• Cost of Model M production for Company B = \(\frac{5}{14} \times 0.896 \text{ crore}\)

Calculation for Company B's Model M cost:

\(\frac{5}{14} \times 0.896 = 5 \times \frac{0.896}{14} = 5 \times 0.064 = 0.320 \text{ crore}\)

So, the production cost for Model M for Company B is Rs. 0.320 crore.

For Company C:

• Production Ratio L:M is 6:5.
• Total parts in ratio = \(6 + 5 = 11\).
• The fraction of cost for Model M is \(\frac{5}{11}\).
• Cost of Model M production for Company C = \(\frac{5}{11} \times \text{Total production cost of C}\)
• Cost of Model M production for Company C = \(\frac{5}{11} \times 1.408 \text{ crore}\)

Calculation for Company C's Model M cost:

\(\frac{5}{11} \times 1.408 = 5 \times \frac{1.408}{11} = 5 \times 0.128 = 0.640 \text{ crore}\)

So, the production cost for Model M for Company C is Rs. 0.640 crore.

Calculating Profit on Model M for Companies B and C

The profit earned on Model M for each company is a percentage of the production cost of Model M.

For Company B:

• Profit percentage on Model M = 30%
• Profit on Model M for Company B = 30% of Cost of Model M production for B
• Profit on Model M for Company B = \(0.30 \times 0.320 \text{ crore}\)

Calculation for Company B's Model M profit:

\(0.30 \times 0.320 = 0.096 \text{ crore}\)

So, the profit on Model M for Company B is Rs. 0.096 crore.

For Company C:

• Profit percentage on Model M = 24%
• Profit on Model M for Company C = 24% of Cost of Model M production for C
• Profit on Model M for Company C = \(0.24 \times 0.640 \text{ crore}\)

Calculation for Company C's Model M profit:

\(0.24 \times 0.640 = 0.1536 \text{ crore}\)

So, the profit on Model M for Company C is Rs. 0.1536 crore.

Calculating Total Profit on Model M for B and C Together

To find the total profit earned by Companies B and C together on Model M, we add their individual profits on Model M.

• Total Profit = Profit on Model M for B + Profit on Model M for C
• Total Profit = \(0.096 \text{ crore} + 0.1536 \text{ crore}\)

Calculation:

\(0.096 + 0.1536 = 0.2496 \text{ crore}\)

The total profit earned by Companies B and C together on Model M is Rs. 0.2496 crore.

Summary of Results

• Production Cost for Company B: Rs. 0.896 crore
• Production Cost for Company C: Rs. 1.408 crore
• Cost of Model M for Company B: Rs. 0.320 crore
• Cost of Model M for Company C: Rs. 0.640 crore
• Profit on Model M for Company B: Rs. 0.096 crore
• Profit on Model M for Company C: Rs. 0.1536 crore
• Total Profit on Model M for B and C: Rs. 0.2496 crore

Revision Table: Key Calculations

Total Profit (B + C) on Model M = \(0.096 + 0.1536 = 0.2496 \text{ crore}\).

Additional Information: Data Interpretation Tips

Data interpretation questions often require careful reading of the table and understanding the relationships between different pieces of information. Here are some tips:

• Always start by reading the title and any accompanying notes or headings to understand what the table represents.
• Identify the specific values needed to answer the question. Ignore irrelevant data.
• Break down multi-step calculations into smaller, manageable steps.
• Pay attention to units (e.g., percentage, ratio, crore rupees) and ensure consistency throughout calculations.
• Use percentages and ratios correctly to find actual values. Remember that a percentage is 'out of 100' and a ratio divides a total quantity into parts.
• Double-check your calculations, especially decimal points.
• Practice different types of data interpretation problems (tables, charts, graphs) to become familiar with common patterns and calculation methods.

This question combined percentage calculations with ratio distribution to find the specific cost and subsequent profit for a particular model within certain companies, based on an overall total cost.