Item Profit Percentage Gain Analysis

This question involves analyzing a table that provides the cost price and sale price for four different items (A, B, C, and D) across several years. The goal is to identify which item demonstrates a specific increase in its profit percentage from the first year (2015) to the last year (2019).

Profit Percentage Calculation Explained

To solve this, we first need to understand how to calculate profit and profit percentage. Profit is the difference between the amount an item is sold for (sale price) and the amount it cost to acquire or produce (cost price). The profit percentage is typically calculated based on the cost price.

The formulas we will use are:

Profit = Sale Price (SP) - Cost Price (CP)

Profit Percentage = $ \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100\% $

The question asks for an item where the profit percentage in the last year (2019) is 10% higher than the profit percentage in the first year (2015). This means the profit percentage in 2019 should be 110% of the profit percentage in 2015.

Mathematically, this condition can be expressed as:

Profit % (2019) = Profit % (2015) $ \times \left(1 + \frac{10}{100}\right) $

Which simplifies to:

Profit % (2019) = Profit % (2015) $ \times 1.10 $

Data Table and Profit Calculations

Let's extract the necessary cost price and sale price data for the years 2015 and 2019 for all items and prepare it for calculation.

Profit Percentage Calculations for 2015 and 2019

Now, we will calculate the profit percentage for each item for both years using the formula: Profit % = $ (\frac{\text{SP} - \text{CP}}{\text{CP}}) \times 100\% $.

Item A Analysis

Year 2015:

• Cost Price (CP) = ₹200000, Sale Price (SP) = ₹230000
• Profit = ₹230000 - ₹200000 = ₹30000
• Profit % = $ \left( \frac{30000}{200000} \right) \times 100\% = 15\% $

Year 2019:

• CP = ₹170000, SP = ₹195500
• Profit = ₹195500 - ₹170000 = ₹25500
• Profit % = $ \left( \frac{25500}{170000} \right) \times 100\% = 15\% $

Check Condition: Does Profit % (2019) = Profit % (2015) $ \times 1.10 $? In this case, $15\% \neq 15\% \times 1.10$ (which equals $16.5\%$). Item A does not satisfy the condition.

Item B Analysis

Year 2015:

• Cost Price (CP) = ₹100000, Sale Price (SP) = ₹110000
• Profit = ₹110000 - ₹100000 = ₹10000
• Profit % = $ \left( \frac{10000}{100000} \right) \times 100\% = 10\% $

Year 2019:

• CP = ₹199500, SP = ₹221445
• Profit = ₹221445 - ₹199500 = ₹21945
• Profit % = $ \left( \frac{21945}{199500} \right) \times 100\% = 11\% $

Check Condition: Does Profit % (2019) = Profit % (2015) $ \times 1.10 $? Here, $11\% = 10\% \times 1.10$. This equation holds true ($0.11 = 0.10 \times 1.10$). Item B satisfies the condition.

Item C Analysis

Year 2015:

• Cost Price (CP) = ₹25000, Sale Price (SP) = ₹28750
• Profit = ₹28750 - ₹25000 = ₹3750
• Profit % = $ \left( \frac{3750}{25000} \right) \times 100\% = 15\% $

Year 2019:

• CP = ₹34000, SP = ₹39100
• Profit = ₹39100 - ₹34000 = ₹5100
• Profit % = $ \left( \frac{5100}{34000} \right) \times 100\% = 15\% $

Check Condition: Does Profit % (2019) = Profit % (2015) $ \times 1.10 $? Here, $15\% \neq 15\% \times 1.10$ (which equals $16.5\%$). Item C does not satisfy the condition.

Item D Analysis

Year 2015:

• Cost Price (CP) = ₹25000, Sale Price (SP) = ₹28750
• Profit = ₹28750 - ₹25000 = ₹3750
• Profit % = $ \left( \frac{3750}{25000} \right) \times 100\% = 15\% $

Year 2019:

• CP = ₹34000, SP = ₹40460
• Profit = ₹40460 - ₹34000 = ₹6460
• Profit % = $ \left( \frac{6460}{34000} \right) \times 100\% = 19\% $

Check Condition: Does Profit % (2019) = Profit % (2015) $ \times 1.10 $? Here, $19\% \neq 15\% \times 1.10$ (which equals $16.5\%$). Item D does not satisfy the condition.

Conclusion: Item with 10% Profit Gain Found

By systematically calculating the profit percentage for each item in 2015 and 2019, and then checking against the condition Profit % (2019) = Profit % (2015) $ \times 1.10 $, we have determined that only Item B meets the specified criteria.