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 $P$ be the price of the item at store M.
Since the price of the item is 10% cheaper in store S compared to store M, the price of the item at store S is:
$P_{\text{S}}=P-0.10P=0.90P$

Now, let us calculate the total cost of purchasing the item from each store, including delivery charges:
• Store S charges ₹150 for delivery, so the total cost at store S is:
${\text{Total Cost}}_{\text{S}}=0.90P+150$
• Store M has no delivery charges, so the total cost at store M is:
${\text{Total Cost}}_{\text{M}}=P$

According to the problem, the person bought the item from store S and saved ₹100. This means the total cost at store S is ₹100 less than the total cost at store M:
${\text{Total Cost}}_{\text{M}}-{\text{Total Cost}}_{\text{S}}=100$
Substituting the expressions into this equation:
$P-(0.90P+150)=100$

We can solve for $P$ step-by-step:
$0.10P-150=100$
Add 150 to both sides of the equation:
$0.10P=250$
Divide by 0.10:
$P=\frac{250}{0.10}=2500$

Thus, the price of the item at store M is ₹2500.
The price of the item at store S ($P_{\text{S}}$) is:
$P_{\text{S}}=0.90\times 2500=2250$

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