If the cost price of 28 oranges is equal to selling price of 24 oranges, then the profit percentage is:

The correct option is:
$16\frac{2}{3}\%$

Let's understand and solve this step-by-step.

Let the cost price (CP) of 1 orange be $x$.
Therefore, the cost price of 28 oranges is:
$\text{CP of 28 oranges}=28x$

According to the problem statement, the cost price of 28 oranges is equal to the selling price (SP) of 24 oranges.
Thus, the selling price of 24 oranges is:
$\text{SP of 24 oranges}=28x$

Now, to calculate the profit or loss, we need to compare the cost price and selling price for the same quantity of oranges.
Let us find the cost price of 24 oranges:
$\text{CP of 24 oranges}=24x$

Since the selling price of 24 oranges ($28x$) is greater than the cost price of 24 oranges ($24x$), there is a profit.
The formula for profit is:
$\text{Profit}=\text{Selling Price (SP)}-\text{Cost Price (CP)}$

For 24 oranges, the profit is:
$\text{Profit}=28x-24x=4x$

Now, we calculate the profit percentage using the formula:
$\text{Profit Percentage}=\left(\frac{\text{Profit}}{\text{Cost Price (CP)}}\right)\times 100$

Substituting the values of profit and CP for 24 oranges into the formula:
$\text{Profit Percentage}=\left(\frac{4x}{24x}\right)\times 100$

Simplifying the fraction:
$\text{Profit Percentage}=\frac{1}{6}\times 100$

Calculating the final value:
$\text{Profit Percentage}=\frac{100}{6}\%=\frac{50}{3}\%$

Converting the improper fraction into a mixed fraction:
$\frac{50}{3}\%=16\frac{2}{3}\%$