On the tag price, a seller offers a 10% discount and a cashback of ₹250. He still earns 10% profit. If the cost price is ₹1,200, then the tag price (rounded off to 2 decimal places) is ₹______.

The correct option is 1744.44.

Let us break down the problem step-by-step to find the tag price (marked price) of the item.

Step 1: Understand the given information
- Cost Price (CP) = ₹1,200
- Profit percentage earned = 10%
- Discount offered on the tag price = 10%
- Cashback offered = ₹250
- Let the tag price (marked price) be denoted as T.

Step 2: Calculate the Selling Price (SP) from the Cost Price and Profit
The seller makes a 10% profit on the cost price.
Selling Price can be calculated using the formula:
$\mathrm{SP}=\mathrm{CP}\times \left(1+\frac{\mathrm{Profit\; \%}}{100}\right)$
Substituting the given values:
$\mathrm{SP}=1200\times \left(1+\frac{10}{100}\right)$
$\mathrm{SP}=1200\times 1.1=1320$
So, the actual Selling Price is ₹1,320.

Step 3: Relate the Selling Price to the Tag Price, Discount, and Cashback
The seller offers a 10% discount on the tag price (T) and then also gives a cashback of ₹250. The amount the customer finally pays (which is the selling price, SP) is given by:
$\mathrm{SP}=\left(T-10\%\text{of}T\right)-\text{Cashback}$
Substituting the values we know:
$1320=\left(T-0.10T\right)-250$
Simplify the equation:
$1320=0.90T-250$

Step 4: Solve for the Tag Price (T)
Add 250 to both sides of the equation:
$1320+250=0.90T$
$1570=0.90T$
Now, divide by 0.90:
$T=\frac{1570}{0.90}$
$T=\frac{15700}{9}$
Calculating the division:
$T\approx \mathrm{1744.4444...}$
Rounding off to two decimal places, we get:
$T=1744.44$

Therefore, the tag price is ₹1,744.44.