Calculating Profit Ratio from Production Data

This problem requires us to analyze the provided table containing data on bicycle production, cost distribution, production ratios, and profit percentages for six different companies (A-F). We need to find the ratio of the profit earned on model L by Company B to the profit earned on model M by Company D.

Let's first look at the data provided in the table:

The total production cost for all six companies combined is given as Rs. 6.4 crore. We can use this information along with the percentage distribution to find the production cost for individual companies.

Step 1: Determine the Production Cost for Company B and Company D

• The total production cost is Rs. 6.4 crore, which is $\text{Rs. } 6.4 \times 10^7$.
• Company B's production accounts for 14% of the total.
• Cost for Company B $= 14\% \text{ of } \text{Rs. } 6.4 \times 10^7 = 0.14 \times 6.4 \times 10^7$.
• Company D's production accounts for 13% of the total.
• Cost for Company D $= 13\% \text{ of } \text{Rs. } 6.4 \times 10^7 = 0.13 \times 6.4 \times 10^7$.

Step 2: Calculate the Cost for Model L (Company B) and Model M (Company D)

The production ratio L:M tells us how the total production (and assuming uniform cost per unit, the total cost) for a company is distributed between the two models.

• For Company B, the production ratio L:M is 9:5. The total parts are $9 + 5 = 14$.
• The cost attributed to Model L for Company B is $\frac{9}{14}$ of Company B's total cost.
• Cost for Model L (Company B) $= \frac{9}{14} \times (0.14 \times 6.4 \times 10^7) = 9 \times 0.01 \times 6.4 \times 10^7 = 0.09 \times 6.4 \times 10^7$.
• For Company D, the production ratio L:M is 6:7. The total parts are $6 + 7 = 13$.
• The cost attributed to Model M for Company D is $\frac{7}{13}$ of Company D's total cost.
• Cost for Model M (Company D) $= \frac{7}{13} \times (0.13 \times 6.4 \times 10^7) = 7 \times 0.01 \times 6.4 \times 10^7 = 0.07 \times 6.4 \times 10^7$.

Step 3: Calculate the Profit for Model L (Company B) and Model M (Company D)

The percentage profit is given for each model and company. Assuming this is percentage profit on cost:

• Company B earns 28% profit on Model L.
• Profit on Model L (Company B) $= 28\% \text{ of } (0.09 \times 6.4 \times 10^7) = 0.28 \times 0.09 \times 6.4 \times 10^7$.
• Company D earns 25% profit on Model M.
• Profit on Model M (Company D) $= 25\% \text{ of } (0.07 \times 6.4 \times 10^7) = 0.25 \times 0.07 \times 6.4 \times 10^7$.

Step 4: Find the Ratio of Profits

We need the ratio of Profit on Model L (Company B) to Profit on Model M (Company D).

Ratio = $\frac{\text{Profit on Model L (Company B)}}{\text{Profit on Model M (Company D)}}$

Ratio = $\frac{0.28 \times 0.09 \times 6.4 \times 10^7}{0.25 \times 0.07 \times 6.4 \times 10^7}$

We can cancel out the common term $6.4 \times 10^7$ from the numerator and denominator.

Ratio = $\frac{0.28 \times 0.09}{0.25 \times 0.07}$

To simplify, we can multiply the numerator and denominator by 10000:

Ratio = $\frac{0.28 \times 0.09 \times 10000}{0.25 \times 0.07 \times 10000} = \frac{(0.28 \times 100) \times (0.09 \times 100)}{(0.25 \times 100) \times (0.07 \times 100)} = \frac{28 \times 9}{25 \times 7}$

Now, we can simplify the expression:

Ratio = $\frac{(4 \times 7) \times 9}{25 \times 7}$

Cancel out the common factor of 7:

Ratio = $\frac{4 \times 9}{25} = \frac{36}{25}$

So, the ratio of the profit earned on model L by Company B to that of model M by Company D is 36:25.

Revision Table: Key Data Points

Ratio of results = $\frac{6.4 \times 10^7 \times 0.14 \times \frac{9}{14} \times 0.28}{6.4 \times 10^7 \times 0.13 \times \frac{7}{13} \times 0.25} = \frac{0.14 \times \frac{9}{14} \times 0.28}{0.13 \times \frac{7}{13} \times 0.25} = \frac{0.01 \times 9 \times 0.28}{0.01 \times 7 \times 0.25} = \frac{9 \times 0.28}{7 \times 0.25} = \frac{9 \times 28}{7 \times 25} = \frac{9 \times 4}{25} = \frac{36}{25}$.

Additional Information on Data Interpretation

Data Interpretation questions often involve extracting information from tables or charts and performing calculations based on percentages, ratios, and totals. Understanding how different percentages or ratios relate to a base value (like total cost or total production) is crucial.

• Percentage Distribution: When a total is distributed among categories, the percentage for each category tells you its proportion of the total. If the total is known, you can find the absolute value for each category.
• Ratios: A ratio like L:M represents the proportion of L to M. If the total for L and M combined is known, you can find the value for L and M individually by dividing the total by the sum of the ratio parts and multiplying by the respective ratio numbers. For example, if the ratio is 9:5, the total is divided into $9+5=14$ parts. L gets 9 parts, and M gets 5 parts.
• Profit Calculation: Profit is typically calculated as a percentage of either the cost price or the selling price. In this question, the context implies profit percentage on cost. Profit = (Profit % / 100) × Cost.
• Calculating Ratios of Derived Values: When asked for the ratio of two calculated values, it's often helpful to set up the expression as a fraction and simplify before multiplying out large numbers, as common terms may cancel out.