Selling Price vs Cost Price Analysis
Let $C$ represent the cost price of one book and $S$ represent the selling price of one book.
The problem states that the selling price (SP) of 40 books is equal to the cost price (CP) of 28 books.
This can be written as an equation:
$ 40 \times S = 28 \times C $
Calculating the Loss Percentage
From the equation, we can find the relationship between $S$ and $C$:
$ S = \frac{28}{40} C $
Simplify the fraction:
$ S = \frac{7}{10} C $
Since the selling price ($S$) is $\frac{7}{10}$ of the cost price ($C$), it means $S < C$. This indicates a loss.
The loss amount for one book is:
$ \text{Loss} = C - S = C - \frac{7}{10} C = \frac{10C - 7C}{10} = \frac{3}{10} C $
To find the loss percentage, we use the formula:
$ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100 $
Substitute the values:
$ \text{Loss Percentage} = \left( \frac{\frac{3}{10} C}{C} \right) \times 100 $
$ \text{Loss Percentage} = \frac{3}{10} \times 100 $
$ \text{Loss Percentage} = 30\% $
Therefore, there is a loss of 30%.
Similar Questions
- I bought two frocks for ₹1,200. I sold the first one at a loss of 7% and the second at a gain of 23%. If, on the whole I made neither a loss nor a gain, find the cost price (in ₹) of the first frock.
- Big Mart is offering $5\%$ discount on card payment. How much percentage above cost price should the marked price be so as to make a profit of $10\%$?
- If a shopkeeper added $20\%$ on the cost price as marked price and gave $20\%$ discount, then how much was his profit or loss percent?
- What is the cost price of articles sold for ₹390 if $20\%$ is the total gain?
- If the selling price of an article is 3 times the discount offered and if the percentage of the discount is equal to the percentage profit, find the ratio of the discount offered to the cost price.
- A vendor purchases an article for ₹500 and sells it for ₹550. What is the percentage gain?
- Rupert purchases a second-hand TV for ₹4,600, spends some money on its repairs, and then sells it for ₹5,406, thereby earning a profit of 6%. How much did Rupert spend on the repairs?
- Atulit buys an old bicycle for ₹4,000 and spends ₹400 towards its repairs. If he sells the bicycle for ₹5,000, his percentage gain is:
- I bought two pendants for ₹1,200. I sold the first one at a loss of 10% and the second at a gain of 14%. If, on the whole I made neither a loss nor a gain, find the cost price (in ₹) of the first pendant.
- The selling price of 10 books is equal to the cost price of 16 books. Find the loss or gain percentage on these books.
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?
By selling a horse for Rs. 670, a tradesman would lose 5%. At what price must he sell it to gain 5%?
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?
