When a discount of $25\%$ is given on a wedding gown, the profit is $32\%$. If the discount is $17\%$, then the profit is ______.

Let the Cost Price (CP) be 100.Since profit is $32\%$, the Selling Price (SP) in the first case is:
$${\text{SP}}_1=100+32=132$$
This selling price is obtained after offering a $25\%$ discount on the Marked Price (MP):
$${\text{SP}}_1=75\%\text{ of MP}$$
$$132=\frac{75}{100}\times \text{MP}=\frac{3}{4}\times \text{MP}$$
$$\text{MP}=\frac{132\times 4}{3}=44\times 4=176$$
Now, in the second scenario, a discount of $17\%$ is given on the Marked Price:
$$\text{New SP }({\text{SP}}_2)=\text{MP}\times (100-17)\%$$
$${\text{SP}}_2=176\times \frac{83}{100}=\frac{14608}{100}=146.08$$
Since $\text{CP}=100$ and ${\text{SP}}_2=146.08$, the new profit percentage is:
$$\text{Profit}\%=146.08-100=46.08\%$$