Profit Percentage Calculation Explained

The problem states that the cost price (CP) of 48 books is equal to the selling price (SP) of 36 books. We need to find the profit percentage.

Relating Cost Price and Selling Price

Let the cost price of one book be $C$ and the selling price of one book be $S$. According to the question:

Cost Price of 48 books = Selling Price of 36 books

This can be written as:

$48 \times C = 36 \times S$

Determining the Ratio of SP to CP

To find the relationship between $S$ and $C$, we rearrange the equation:

$\frac{S}{C} = \frac{48}{36}$

Simplify the fraction:

$\frac{S}{C} = \frac{4}{3}$

This ratio means that for every $3$ units of cost price, the selling price is $4$ units.

Calculating Profit Percentage

Profit is defined as Selling Price minus Cost Price ($S - C$). The profit percentage is calculated using the formula:

$\text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost Price}} \times 100\%$

$\text{Profit Percentage} = \frac{S - C}{C} \times 100\%$

Substitute the ratio $\frac{S}{C} = \frac{4}{3}$ into the formula:

$\text{Profit Percentage} = \left( \frac{S}{C} - \frac{C}{C} \right) \times 100\%$

$\text{Profit Percentage} = \left( \frac{4}{3} - 1 \right) \times 100\%$

$\text{Profit Percentage} = \left( \frac{4}{3} - \frac{3}{3} \right) \times 100\%$

$\text{Profit Percentage} = \frac{1}{3} \times 100\%$

$\text{Profit Percentage} = 33.333...\%$

Final Answer Formatting

Rounding the result to two decimal places, the profit percentage is $33.33\%$.