The price of an item is 10% cheaper in an online store S compared to the price at another online store M.Store S charges ₹ `150 for delivery. There are no delivery charges for orders from the store M. A person bought the item from the store S and saved `₹100. What is the price of the item at the online store S (in ₹`) if there are no other charges than what is described above?

The correct option is 2250.

Let the price of the item at the online store M be represented as P_M.
According to the problem, the price of the item at the online store S is 10% cheaper than at store M. Therefore, we can write the price at store S (P_S) as:
$P_S=P_M-0.10P_M=0.90P_M$

Now, let's consider the total cost of purchasing the item from each store, including delivery charges:
- At store M, there are no delivery charges, so the total cost is simply the price of the item:
${\text{Total Cost}}_M=P_M$
- At store S, there is a delivery charge of ₹ 150, so the total cost is:
${\text{Total Cost}}_S=P_S+150=0.90P_M+150$

The problem states that a person bought the item from store S and saved ₹ 100 compared to buying it from store M. This means:
${\text{Total Cost}}_M-{\text{Total Cost}}_S=100$

Substitute the expressions for the total costs into the savings equation:
$P_M-(0.90P_M+150)=100$

Simplify the equation to find the value of P_M:
$0.10P_M-150=100$
Add 150 to both sides:
$0.10P_M=250$
Multiply both sides by 10 to solve for P_M:
$P_M=2500$

Thus, the price of the item at online store M is ₹ 2500.
We need to find the price of the item at online store S. Since P_S is 10% cheaper than P_M:
$P_S=0.90\times 2500=2250$

Therefore, the price of the item at the online store S is ₹ 2250.