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:

$Gain \% = \left(\frac{1 \text{ unit}}{5 \text{ units}}\right) \times 100\%$

$Gain \% = \frac{1}{5} \times 100\%$

$Gain \% = 20\%$