Ravi sells a smartphone for Rs. 30,000. If he had offered a discount of 10% on this selling price, he would still have earned a profit of 35%. What is the original cost price of the smartphone?

Introduction / Context:
This question blends the ideas of marked price, discount, and profit. Ravi sells a smartphone at a certain price but is asked to consider a hypothetical scenario where he gives a discount on this selling price and still makes a profit. We must work backwards from this hypothetical situation to find the true cost price of the phone. Such questions test comfort with reversing percentage calculations and dealing with multiple conditions around the same cost price.

Given Data / Assumptions:

• Actual selling price (SP1) of the smartphone = Rs. 30,000.
• If Ravi had given a discount of 10% on Rs. 30,000, then the selling price in that case (SP2) would be 90% of 30,000.
• At this discounted selling price, Ravi would have made a profit of 35% on cost price.
• Let the cost price be C.
• We need to find C.

Concept / Approach:
The structure is: discounted selling price = cost price * (1 + profit%). We know the discounted selling price indirectly as 90% of the original selling price. So we first compute the hypothetical discounted price, then equate it to 1.35 * C because a 35% profit means the selling price equals 135% of cost price. Solving this equation yields the cost price. Note that the original selling price of 30,000 is not used directly to find profit; it only helps us find the hypothetical discount price.

Step-by-Step Solution:
Original selling price SP1 = Rs. 30,000.If a discount of 10% is offered on this, then the new selling price SP2 would be SP1 * 0.90.Compute SP2: 30000 * 0.90 = Rs. 27,000.We are told that at this price Ravi would earn a 35% profit on cost price.So SP2 = C * 1.35.Therefore, 1.35 * C = 27,000.C = 27,000 / 1.35.Compute C = Rs. 20,000.Thus, the cost price of the smartphone is Rs. 20,000.

Verification / Alternative check:
With cost price C = Rs. 20,000, a 35% profit implies SP2 = 1.35 * 20000 = Rs. 27,000.This SP2 is exactly 90% of Rs. 30,000, which matches the discount description.So if he had sold at Rs. 27,000, he would have a 35% profit, as required.

Why Other Options Are Wrong:
If C = Rs. 22,000, then 35% profit would give SP2 = 29,700, not equal to 27,000.If C = Rs. 24,000, then SP2 = 32,400, which again does not match the needed 27,000.If C = Rs. 26,000, then SP2 = 35,100, also inconsistent with the condition.Only Rs. 20,000 satisfies the relationship between discounted selling price and profit.

Common Pitfalls:
Some students mistakenly apply the 35% profit to the original selling price instead of the cost price.Another common error is to compute the discount on the cost price, even though the question clearly applies it to the selling price.Not carefully distinguishing between SP1 and SP2 often leads to incorrect equations and wrong answers.

Final Answer:
The original cost price of the smartphone is Rs. 20,000.