Analyzing Sales and Profit Increase for HP-Showroom D (2020-2021)

The question asks for the ratio of the percentage increase in sales to the percentage increase in profit for HP-Showroom D from 2020 to 2021. We need to use the data provided in the table for Showroom D.

Extracting Data for HP-Showroom D

Let's first pull the relevant figures for Showroom D from the table:

Calculating Total Sales for HP-Showroom D

Total sales for a showroom is calculated by multiplying the number of outlets by the average sales per outlet.

• Total Sales in 2020 = Number of Outlets (2020) $\times$ Average Sales per Outlet (2020)
• Total Sales in 2021 = Number of Outlets (2021) $\times$ Average Sales per Outlet (2021)

Let's calculate the total sales for Showroom D:

• Total Sales (2020) = $5 \times 180 = 900$ Rs. Lakh
• Total Sales (2021) = $6 \times 240 = 1440$ Rs. Lakh

Calculating Percentage Increase in Sales

The percentage increase in sales is calculated using the formula:

$$ \text{Percentage Increase in Sales} = \left( \frac{\text{Sales}_{2021} - \text{Sales}_{2020}}{\text{Sales}_{2020}} \right) \times 100 $$

Let's calculate the percentage increase in sales for Showroom D:

$$ \text{Percentage Increase in Sales} = \left( \frac{1440 - 900}{900} \right) \times 100 $$

$$ \text{Percentage Increase in Sales} = \left( \frac{540}{900} \right) \times 100 $$

$$ \text{Percentage Increase in Sales} = \frac{54}{90} \times 100 $$

$$ \text{Percentage Increase in Sales} = \frac{6}{10} \times 100 $$

$$ \text{Percentage Increase in Sales} = 0.6 \times 100 = 60\% $$

Calculating Percentage Increase in Profit

The percentage increase in profit is calculated using the formula:

$$ \text{Percentage Increase in Profit} = \left( \frac{\text{Profit}_{2021} - \text{Profit}_{2020}}{\text{Profit}_{2020}} \right) \times 100 $$

We already have the total profit figures for Showroom D:

• Total Profit (2020) = 240 Rs. Lakh
• Total Profit (2021) = 360 Rs. Lakh

Let's calculate the percentage increase in profit:

$$ \text{Percentage Increase in Profit} = \left( \frac{360 - 240}{240} \right) \times 100 $$

$$ \text{Percentage Increase in Profit} = \left( \frac{120}{240} \right) \times 100 $$

$$ \text{Percentage Increase in Profit} = \frac{1}{2} \times 100 $$

$$ \text{Percentage Increase in Profit} = 0.5 \times 100 = 50\% $$

Calculating the Ratio of Percentage Increases

The question asks for the ratio of the percentage increase in sales to the percentage increase in profit.

$$ \text{Ratio} = \frac{\text{Percentage Increase in Sales}}{\text{Percentage Increase in Profit}} $$

$$ \text{Ratio} = \frac{60\%}{50\%} = \frac{60}{50} = \frac{6}{5} $$

The ratio is $6:5$.

Conclusion

The ratio of percentage increase in sales to the percentage increase in profit for HP-Showroom D in 2021 over 2020 is $6:5$. This corresponds to Option 4.

Revision Table: HP-Showroom D Analysis

Additional Information: Data Interpretation and Percentage Change

Understanding how to interpret data from tables and calculate percentage changes is crucial for data interpretation questions. A percentage change tells us the relative increase or decrease of a value compared to its initial value.

• The formula for percentage change is $\left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100$.
• A positive result indicates a percentage increase, while a negative result indicates a percentage decrease.
• In this problem, we calculated the total sales based on the number of outlets and average sales, which is a common step in data interpretation problems involving aggregated data.
• Ratios help compare two quantities. Here, we compared the magnitude of the percentage increase in sales relative to the percentage increase in profit for the same entity (HP-Showroom D) over the same period.