A book seller purchased 800 copies of a book for ₹4,400. He sold 600 copies at a profit of 20% and the remaining copies at a loss of 5%. Find the percent profit/loss in the total t... A book seller purchased 800 copies of a book for ₹4,400. He sold 600 copies at a profit of 20% and the remaining copies at a loss of 5%. Find the percent profit/loss in the total transaction.
Understand the Problem
The question asks for the calculation of the percent profit or loss based on the sale of books, detailing both the profit made from selling 600 copies and the loss on the remaining copies. The total cost is provided, and the problem involves finding the overall profit or loss percentage of the transaction.
Answer
The percent profit in the total transaction is approximately $13.77\%$.
Answer for screen readers
The percent profit in the total transaction is approximately $13.77%$.
Steps to Solve
- Calculate the cost per book
The total cost of the books is ₹4,400. Since 800 copies were bought:
$$ \text{Cost per book} = \frac{4400}{800} = 5.5 \text{ (₹)} $$
- Determine the selling price for the 600 copies sold at a profit of 20%
To find the selling price (SP) for these copies, apply the profit percentage:
$$ \text{SP} = \text{Cost} + \text{Profit} = \text{Cost} + (0.20 \times \text{Cost}) $$
Using the cost per book:
$$ \text{SP}_1 = 5.5 + (0.20 \times 5.5) = 5.5 + 1.1 = 6.6 \text{ (₹)} $$
- Calculate the total selling price for the 600 copies
$$ \text{Total SP for 600 copies} = 600 \times 6.6 = 3960 \text{ (₹)} $$
- Determine the selling price for the remaining 200 copies sold at a loss of 5%
The selling price for these copies is:
$$ \text{SP}_2 = \text{Cost} - \text{Loss} = \text{Cost} - (0.05 \times \text{Cost}) $$
Using the cost per book:
$$ \text{SP}_2 = 5.5 - (0.05 \times 5.5) = 5.5 - 0.275 = 5.225 \text{ (₹)} $$
- Calculate the total selling price for the 200 copies
$$ \text{Total SP for 200 copies} = 200 \times 5.225 = 1045 \text{ (₹)} $$
- Calculate the overall total selling price
$$ \text{Total SP} = \text{Total SP for 600 copies} + \text{Total SP for 200 copies} $$ $$ \text{Total SP} = 3960 + 1045 = 5005 \text{ (₹)} $$
- Determine the overall profit or loss
Calculate the profit or loss by subtracting the total cost from the total selling price:
$$ \text{Profit/Loss} = \text{Total SP} - \text{Total Cost} $$ $$ \text{Profit/Loss} = 5005 - 4400 = 605 \text{ (₹)} $$
- Calculate the percent profit/loss
The percentage profit is given by:
$$ \text{Percent Profit} = \left( \frac{\text{Profit}}{\text{Total Cost}} \right) \times 100 $$
$$ \text{Percent Profit} = \left( \frac{605}{4400} \right) \times 100 \approx 13.77% $$
The percent profit in the total transaction is approximately $13.77%$.
More Information
This calculation shows how combining profits and losses from different sales impacts the overall financial outcome of a transaction. Understanding profit margins is crucial for evaluating business success.
Tips
- Not calculating the cost per book correctly: Ensure the total cost is divided by the correct number of copies.
- Neglecting to convert profit or loss percentages to actual monetary values: Always find the actual selling price before calculating the total profit or loss.
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