The selling price of 20 books is equal to the cost price of 31 books. Find the loss or gain percentage.

The correct option is 55 % gain.

Let us solve this step-by-step to find the gain or loss percentage.

Step 1: Express the given relationship mathematically.
Let the Cost Price of 1 book be $CP$ and the Selling Price of 1 book be $SP$.

According to the problem, the selling price of 20 books is equal to the cost price of 31 books:

$20\times SP=31\times CP$

Step 2: Find the ratio of Selling Price to Cost Price.
Rearranging the equation to find the ratio $\frac{SP}{CP}$:

$\frac{SP}{CP}=\frac{31}{20}$

This means for every 20 units of Cost Price, the Selling Price is 31 units.

Step 3: Determine Gain or Loss.
Since $SP>CP$, there is a profit (gain).

$\text{Gain}=SP-CP$

Using the ratio values ($SP=31$ and $CP=20$):

$\text{Gain}=31-20=11$

Step 4: Calculate the Gain Percentage.
The formula for gain percentage is:

$\text{Gain \%}=\left(\frac{\text{Gain}}{CP}\right)\times 100$

Substitute the values into the formula:

$\text{Gain \%}=\left(\frac{11}{20}\right)\times 100$

$\text{Gain \%}=11\times 5=55\%$

Hence, the gain percentage is 55 % gain.