Cost Price (CP) Calculation
The total cost incurred by the software company for developing 800 licenses is provided.
Cost Price (CP) = ₹4,000,000
License Distribution Analysis
To calculate revenue, we first determine the number of licenses sold versus those given away.
- Total Licenses Developed: 800
- Licenses Provided Free (Beta Testers): 50
- Remaining Licenses for Sale/Distribution: $800 - 50 = 750$
The offer '1 license free for every 9 licenses bought' means that for every block of 10 licenses distributed under this offer, 9 are paid and 1 is free. Let N represent the number of licenses paid for.
The quantity of free licenses obtained through this offer is $\lfloor N/9 \rfloor$.
The total count of distributed licenses is the sum of paid licenses, free offer licenses, and free beta tester licenses:
Total Distributed = $N + \lfloor N/9 \rfloor + 50$
Given that all 800 licenses were distributed:
$N + \lfloor N/9 \rfloor + 50 = 800$
Simplifying, we get:
$N + \lfloor N/9 \rfloor = 750$
Solving this equation yields N = 675. Thus, 675 licenses were paid for.
Number of free licenses (offer) = $\lfloor 675 / 9 \rfloor = 75$.
Verification: $675$ (paid) + $75$ (free offer) + $50$ (beta) = $800$ total licenses.
Selling Price (SP) and Revenue Calculation
Revenue is calculated based on the price obtained for the paid licenses after discounts.
Market Price per license = ₹6000
Discount offered = 15%
Discount amount calculation:
Discount = $0.15 \times 6000 = 900$
Discounted Selling Price per license = $6000 - 900 = 5100$
Total Revenue (SP) = Number of Paid Licenses $\times$ Discounted Selling Price per license
Total Revenue (SP) = $675 \times 5100 = 3,442,500$
Profit or Loss Determination
Profit or Loss is the difference between Total Revenue (SP) and Total Cost Price (CP).
Profit/Loss = Total Revenue (SP) - Total Cost Price (CP)
Profit/Loss = $3,442,500 - 4,000,000 = -557,500$
A negative value indicates a loss.
Total Loss Amount = ₹557,500
Loss Percentage Calculation
The loss percentage quantifies the loss relative to the initial cost.
Loss Percentage = $\frac{Loss Amount}{Cost Price} \times 100$
Loss Percentage = $\frac{557,500}{4,000,000} \times 100$
Loss Percentage = $0.139375 \times 100 = 13.9375\%$
Final Gain or Loss Percentage
Rounding the calculated loss percentage to two decimal places provides the final answer.
Overall Loss Percentage ≈ 13.94%.
Similar Questions
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Important Questions from Profit and Loss
By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?
By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?
The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?
A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
