The problem requires calculating the gain percentage based on a relationship between the cost price (CP) and selling price (SP) of books.
Gain Percent Calculation
We are given the condition that the cost price of 72 books is equal to the selling price of 60 books.
Let $CP_{unit}$ represent the cost price of a single book and $SP_{unit}$ represent the selling price of a single book.
Mathematically, this can be stated as:
$72 \times CP_{unit} = 60 \times SP_{unit}$
Deriving Price Ratio
To determine the gain, we need to find the ratio between the cost price and the selling price.
Rearranging the equation gives us:
$\frac{CP_{unit}}{SP_{unit}} = \frac{60}{72}$
Simplifying this fraction by dividing both numerator and denominator by their greatest common divisor (12):
$\frac{CP_{unit}}{SP_{unit}} = \frac{5}{6}$
This ratio means that for every 5 units of cost price, the selling price is 6 units.
Calculating Gain Percent
We can establish a baseline for calculation:
- Assume Cost Price (CP) = 5 units
- Assume Selling Price (SP) = 6 units
Gain is calculated as the difference between the selling price and the cost price:
$Gain = SP - CP$
$Gain = 6 \text{ units} - 5 \text{ units} = 1 \text{ unit}$
The formula for gain percent is:
$Gain \% = \left(\frac{Gain}{CP}\right) \times 100\%$
Substitute the values we found:
$Gain \% = \left(\frac{1 \text{ unit}}{5 \text{ units}}\right) \times 100\%$
$Gain \% = \frac{1}{5} \times 100\%$
$Gain \% = 20\%$
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?
