Calculate Speaker Profit Percentage
This solution calculates the store's actual profit percentage based on the sales of portable speakers.
1. Calculate Total Investment
The total cost (investment) is the number of speakers ordered multiplied by the cost per speaker.
- Number of speakers ordered: 150
- Cost per speaker: ₹400
- Total Investment = $150 \times \text{₹}400 = \text{₹}60,000$
2. Determine Target Revenue for 40% Profit
The owner wants a 40% profit on the total investment, even if only 120 speakers are sold.
- Target Profit = $40\% \text{ of Total Investment}$
- Target Profit = $0.40 \times \text{₹}60,000 = \text{₹}24,000$
- Target Revenue (from 120 speakers) = Total Investment + Target Profit
- Target Revenue = $\text{₹}60,000 + \text{₹}24,000 = \text{₹}84,000$
3. Calculate Required Selling Price Per Speaker
To achieve the target revenue by selling 120 speakers, we find the price per speaker.
- Selling Price (SP) per speaker = Target Revenue / Number of speakers sold for target
- SP per speaker = $\text{₹}84,000 / 120 = \text{₹}700$
4. Calculate Actual Revenue
The store actually sold 135 speakers at the calculated selling price. The remaining speakers have no value.
- Actual speakers sold: 135
- Selling Price per speaker: ₹700
- Actual Revenue = $135 \times \text{₹}700 = \text{₹}94,500$
5. Calculate Actual Profit
The actual profit is the actual revenue minus the total investment.
- Actual Profit = Actual Revenue - Total Investment
- Actual Profit = $\text{₹}94,500 - \text{₹}60,000 = \text{₹}34,500$
6. Calculate Actual Profit Percentage
The actual profit percentage is calculated based on the total investment.
- Actual Profit Percentage = $\left( \frac{\text{Actual Profit}}{\text{Total Investment}} \right) \times 100$
- Actual Profit Percentage = $\left( \frac{\text{₹}34,500}{\text{₹}60,000} \right) \times 100$
- Actual Profit Percentage = $\frac{345}{600} \times 100 = \frac{115}{200} \times 100 = 57.5\%$
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