A trader sells one item to a retailer at a $20\%$ discount, but charges $10\%$ on the discounted price, for delivery and packaging. The retailer sells it for $\text{₹}4,092$ more, thereby earning a profit of $25\%$. At what price had the trader marked the item?

Let the Marked Price ($\text{MP}$) set by the trader be $x$.
* The trader gives a $20\%$ discount, so the discounted price $=0.80x$.
* The trader adds a $10\%$ charge on this discounted price for delivery and packaging.
* Thus, the final price paid by the retailer (which is the retailer's Cost Price, ${\text{CP}}_{\text{retailer}}$) is:

$${\text{CP}}_{\text{retailer}}=0.80x\times (1+0.10)=0.80x\times 1.1=0.88x$$

The retailer sells the item for $\text{₹}4,092$ more than their cost price. This markup/increase is their absolute profit amount:

$$\text{Profit amount}=\text{₹}4,092$$

We are given that the retailer earns a profit percentage of $25\%$:

$$\text{Profit }\%=\frac{\text{Profit amount}}{{\text{CP}}_{\text{retailer}}}\times 100\%$$

$$25\%=\frac{4,092}{0.88x}\times 100\%$$

$$0.25=\frac{4,092}{0.88x}$$

$$0.25\times 0.88x=4,092$$

$$0.22x=4,092$$

$$x=\frac{4,092}{0.22}=\frac{409200}{22}=\text{₹}18,600$$

Thus, the marked price of the item was $\text{₹}18,600$.