A fruit seller buys some oranges at the rate of $4$ for $\text{₹ }10$ and an equal number more at $5$ for $\text{₹ }10$. Then he sells the whole lot at the rate of $9$ for $\text{₹ }20$. What is his loss or gain percentage?

To simplify calculation, assume the number of oranges bought of each type is the LCM of the quantities $4$, $5$, and $9$.
$$\text{LCM}(4,5,9)=180$$

Let him buy $180$ oranges of the first type and $180$ oranges of the second type.
Total oranges bought $=180+180=360$

**Step 1: Calculate the total Cost Price ($\text{CP}$)**

* Cost of first type ($4$ oranges for $\text{₹ }10$):

$${\text{CP}}_1=\frac{10}{4}\times 180=\text{₹ }450$$

* Cost of second type ($5$ oranges for $\text{₹ }10$):

$${\text{CP}}_2=\frac{10}{5}\times 180=\text{₹ }360$$

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

$$\text{Total CP}=450+360=\text{₹ }810$$

**Step 2: Calculate the total Selling Price ($\text{SP}$)**

* He sells the whole lot ($360$ oranges) at the rate of $9$ for $\text{₹ }20$:

$$\text{Total SP}=\frac{20}{9}\times 360=20\times 40=\text{₹ }800$$

Step 3: Calculate Loss Percentage
Since $\text{Total CP}>\text{Total SP}$, there is a loss.

$$\text{Loss}=\text{Total CP}-\text{Total SP}=810-800=\text{₹ }10$$

$$\text{Loss Percentage}=\left(\frac{\text{Loss}}{\text{Total CP}}\times 100\right)\%$$

$$\text{Loss Percentage}=\left(\frac{10}{810}\times 100\right)\%=\frac{100}{81}\%=1\frac{19}{81}\%$$

Thus, there is a loss of $1\frac{19}{81}\%$.