After selling $110\text{ oranges}$, a shopkeeper claims that he makes a profit equal to the selling price of $22\text{ oranges}$. Find the profit percentage of the shopkeeper.

Let the Selling Price ($\text{SP}$) of $1\text{ orange}$ be \ 1$.Then,theSellingPriceof$ 110\text{ oranges}$($ \text{SP}_{110}$)=$ \$110$.

According to the question, the profit is equal to the selling price of $22\text{ oranges}$:

$$\text{Profit}=\$22$$

We know that:

$$\text{Cost Price (CP)}=\text{SP}-\text{Profit}$$

$$\text{CP}=110-22=\$88$$

Now, calculate the profit percentage:

$$\text{Profit Percentage}=\left(\frac{\text{Profit}}{\text{CP}}\right)\times 100$$

$$\text{Profit Percentage}=\left(\frac{22}{88}\right)\times 100=\frac{1}{4}\times 100=25\%$$