Understanding the Book Transaction Problem
This problem involves calculating the percentage gain made on a book transaction. We are given the buying price relative to the listed price and the selling price relative to the listed price. We need to determine the overall profit percentage.
Step-by-Step Solution
1. Define Variables and Assume a Listed Price
To make calculations easier, let's assume the Listed Price (LP) of the book is $100.
- Listed Price (LP) = $100
2. Calculate the Buying Price (BP)
The person bought the book at \(\frac{3}{4}^{th}\) of its listed price.
- Buying Price (BP) = \((\frac{3}{4}) \times \text{Listed Price}\)
- BP = \((\frac{3}{4}) \times 100\)
- BP = $75
So, the cost price for the person was $75.
3. Calculate the Selling Price (SP)
The book was sold at 50% more than its listed price.
- Selling Price (SP) = \(\text{Listed Price} + 50\% \text{ of Listed Price}\)
- SP = \(100 + (\frac{50}{100}) \times 100\)
- SP = \(100 + 50\)
- SP = $150
So, the selling price of the book was $150.
4. Calculate the Gain
The gain is the difference between the selling price and the buying price.
- Gain = Selling Price (SP) - Buying Price (BP)
- Gain = \(150 - 75\)
- Gain = $75
5. Calculate the Percentage Gain
The percentage gain is calculated based on the buying price (cost price).
- Percentage Gain = \((\frac{\text{Gain}}{\text{Buying Price (BP)}}) \times 100\%\)
- Percentage Gain = \((\frac{75}{75}) \times 100\%\)
- Percentage Gain = \(1 \times 100\%\)
- Percentage Gain = $100\%
Conclusion
The percentage of gain in the transaction is 100%.
Important Questions from Profit and Loss
Ram bought a chair at 35% discount on its market price, Had Ram got no discount, he would have had to pay ₹245 more. How much did Ram pay for the chair?
A shopkeeper bought an item for Rs. 4,500 and sold it at a loss of 5%. From this money, he bought another item and sold it at a profit of 10%. What is his overall profit?
A man sells two articles at Rs. 9,180 each. He gains 8% on one article and loses 15% on the other. His overall profit or loss is:
A shopkeeper selling an article for ₹46 loses 8%. In order to gain 6%, what should be the selling price of the article?
Rahul purchased 80 items from the market. 25% items of the total items were defective and the remaining items were sold at 50% profit. What will be the overall profit percentage?
