If $3$ mangoes are sold for the cost price of $4$ mangoes, then the profit is

Let the Cost Price ($\text{CP}$) of $1$ mango be $x$.
Then, the Cost Price of $3$ mangoes $=3x$.

According to the question, the Selling Price ($\text{SP}$) of $3$ mangoes equals the Cost Price of $4$ mangoes:

$$\text{SP of }3\text{ mangoes}=4x$$

Now, calculate the profit generated on selling these $3$ mangoes:

$$\text{Profit}=\text{SP}-\text{CP}=4x-3x=x$$

Calculate the profit percentage:

$$\text{Profit Percentage}=\left(\frac{\text{Profit}}{\text{CP of }3\text{ mangoes}}\right)\times 100$$

$$\text{Profit Percentage}=\frac{x}{3x}\times 100=\frac{100}{3}\%=33\frac{1}{3}\%$$