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%.
Similar Questions
- The cost price of \(y\) articles is equal to selling price of \(z\) articles. If \(y:z = 5:4\), what is the profit percentage?
- A shopkeeper gives three consecutive discounts 10%, 20% and 25% after which he sells the article at a profit of 8% on the cost price. Had he sold the article after the first discount, how much profit would he have got?
A person sells article X for ₹34,500 and makes a profit of 15%. He sells article Y at a loss of 10%. He neither loses nor gains on the whole because of these two transactions. What is the selling price of article Y?
A shopkeeper sold his goods at the cost price. By using false weights, he gained \(11\frac{1}{9}\%\). What weight did he use for 1 kg?
The ratio of the cost price of two articles X and Y is \(1:2\). A businessman earns a profit of \(p\%\) by selling X and a loss of \(3p\%\) by selling Y. If he loses \(20\%\) in this transaction, then what is the value of \(p\)?
Important Questions from Profit and Loss
Rohit buys 8 pens and 4 pencils for Rs. 2400. He sells pencils at a profit of 20 percent and pens at the loss of 10 percent. If his overall profit is Rs. 240, then what is the sum of the cost price of one pen and one pencil?
A man sells a car to his friend at the loss of 10 %; who in return sells it for Rs. 54000 making a profit of 20 %. What was the initial value of the car?
An article was sold at a loss of 24%. If it were sold for Rs. 1,596 more, then there would have been a gain of 18%, The cost price of the article is:
The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?
If the selling price of 7 articles is equal to the cost price of 6 articles, then what is the percentage loss?
