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.
- I bought two toy guns for ₹1,200. I sold the first one at a loss of 8% and the second at a gain of 16%. If, on the whole I made neither a loss nor a gain, find the cost price (in ₹) of the first toy gun.
- By selling $50$ mangoes for $₹30$, a person loses $10\%$. How many mangoes should he sell for $₹28$ to gain $20\%$?
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- X purchased a car at ₹ 1,50,000 and then sold it to Y at a profit of 5%. Y later sold it back to X at a loss of 2%. Find the overall profit or loss for X in the entire transaction
- The cost price of a car was ₹1,50,000. It was sold by X at a profit of 5% to Y. It was later sold back to X by Y at a 1% loss. Find X's profit in the entire transaction.
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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?
