A man buys two types of oranges equal in number, one at $5$ for a rupee and the other at $3$ for a rupee, and sells the entire lot at $6$ for $\text{Rs. }2$. His gain or loss percent is:

Let the man buy $15$ oranges of each type (since $15$ is the LCM of $5$ and $3$).
Total oranges bought = $15+15=30$ oranges.

* Cost Price ($\text{CP}$) of the first type ($5$ for $\text{Rs. }1$):

$${\text{CP}}_1=\frac{1}{5}\times 15=\text{Rs. }3$$

* Cost Price ($\text{CP}$) of the second type ($3$ for $\text{Rs. }1$):

$${\text{CP}}_2=\frac{1}{3}\times 15=\text{Rs. }5$$

* Total Cost Price ($\text{Total CP}$):

$$\text{Total CP}=3+5=\text{Rs. }8$$

He sells the whole lot at $6$ for $\text{Rs. }2$ (which is $\text{Rs. }\frac{2}{6}=\text{Rs. }\frac{1}{3}$ per orange).

* Total Selling Price ($\text{Total SP}$) for $30$ oranges:

$$\text{Total SP}=\frac{2}{6}\times 30=\text{Rs. }10$$

Now compute the gain or loss:

$$\text{Gain}=\text{Total SP}-\text{Total CP}=10-8=\text{Rs. }2$$

$$\text{Gain }\%=\left(\frac{\text{Gain}}{\text{Total CP}}\right)\times 100\%=\left(\frac{2}{8}\right)\times 100\%=25\%\text{ gain}$$