A shopkeeper allows a discount of $10\%$ on the marked price of an item but charges a sales tax of $8\%$ on the discounted price. If the customer pays $₹34,020$ as the price including the sales tax, then what is the marked price?

Let the marked price of the item be $M$.
Step 1: Express the discounted price
The shopkeeper gives a discount of $10\%$.

$$\text{Discounted Price}=M-10\%\text{ of }M=0.90M$$

Step 2: Express the final price including sales tax
A sales tax of $8\%$ is charged on this discounted price.

$$\text{Final Price}=\text{Discounted Price}\times \left(1+\frac{8}{100}\right)$$

$$\text{Final Price}=0.90M\times 1.08$$

**Step 3: Solve for $M$ using the given final price**
Given that the customer pays $₹34,020$:

$$0.90M\times 1.08=34,020$$

$$0.972M=34,020$$

$$M=\frac{34,020}{0.972}$$

$$M=\frac{34,020\times 1000}{972}$$

Let's simplify by dividing $34,020$ by $972$:

$$34,020÷972=35$$

Therefore,

$$M=35\times 1,000=₹35,000$$

Thus, the marked price is $₹35,000$.