A shopkeeper sells a mobile phone for Rs 12,000. Had he offered a discount of 10% on this selling price, he would have incurred a loss of 4%. What is the cost price of the mobile phone?

Introduction / Context:
This question mixes a given selling price with a hypothetical discounted selling price that would result in a loss. By working backward from the hypothetical case, we can determine the cost price. This structure is common in exam problems, where you must convert a worded condition about possible discounts and losses into clear algebraic steps.

Given Data / Assumptions:

• Actual selling price of the mobile phone SP₁ = Rs 12,000.
• If a discount of 10% had been offered on this price, the phone would have been sold at SP₂ = 90% of 12,000.
• At SP₂, the shopkeeper would have incurred a loss of 4%.
• Cost price (CP) is the same in both scenarios.
• We must find the cost price of the phone.

Concept / Approach:
A 10% discount on the given selling price means the hypothetical selling price SP₂ is 0.9 * 12,000. At that price, the shopkeeper loses 4%, so SP₂ equals 96% of CP, or SP₂ = 0.96 * CP. This equation allows us to solve for CP. Once CP is known, we can confirm that selling at 12,000 would indeed yield a profit rather than a loss, consistent with the scenario.

Step-by-Step Solution:
Step 1: Actual selling price SP₁ = 12,000.Step 2: If a 10% discount were given, hypothetical selling price SP₂ = 0.9 * 12,000 = Rs 10,800.Step 3: At SP₂, there would be a loss of 4%, so SP₂ = 0.96 * CP.Step 4: Therefore, 10,800 = 0.96 * CP.Step 5: CP = 10,800 / 0.96 = Rs 11,250.

Verification / Alternative check:
With CP = 11,250, selling at SP₂ = 10,800 gives loss = 11,250 - 10,800 = 450. Loss% = (450 / 11,250) * 100 = 4%. Selling at the original price of 12,000 gives profit = 12,000 - 11,250 = 750. Profit% = (750 / 11,250) * 100 ≈ 6.67%. Both percentages match the intended conditions, confirming that the cost price is Rs 11,250.

Why Other Options Are Wrong:
Cost price values like Rs 12,500, Rs 12,750 and Rs 11,680 do not yield a 4% loss at the discounted price of Rs 10,800. For example, if CP were 12,500, loss at 10,800 would be 1,700, giving a loss percentage of 13.6%, not 4%. Only Rs 11,250 fits the equation 10,800 = 0.96 * CP and the resulting percentages correctly.

Common Pitfalls:
Students sometimes apply the 10% discount to cost price instead of the given selling price, or they treat the 4% loss as being on the selling price. Another error is to think that the 10% and 4% can be combined or averaged. Always apply each percentage to its proper base: discount on selling price or marked price, and loss percentage on cost price.

Final Answer:
The cost price of the mobile phone is Rs. 11,250.