A man bought an article and sold it at a gain of 5%. If he had bought it at 5% less than the original cost price and sold it for Re. 1 less than the original selling price, he would have made a profit of 10%. What was the original cost price of the article?

Introduction / Context:
This is a classic reverse-calculation problem in profit and loss. Two hypothetical scenarios are given, each with different buying and selling conditions and different profit percentages. The question asks for the original cost price. It tests the ability to set up and solve equations using percentage gain and small absolute changes in buying and selling prices.

Given Data / Assumptions:

• Original cost price = C (unknown).
• Original selling price gives a profit of 5%.
• In an alternate scenario, cost price is reduced by 5% and selling price is reduced by Re. 1.
• In the alternate scenario, the profit is 10% on the reduced cost price.
• We must find C, the original cost price.

Concept / Approach:
Let the original cost price be C. Then original selling price S1 = 1.05C. In the second scenario, the new cost price is 0.95C and the new selling price is S1 - 1. The problem states that this new selling price corresponds to a 10% gain on 0.95C, so it must equal 1.10 * 0.95C. Equating S1 - 1 with 1.10 * 0.95C gives an equation involving C that can be solved directly.

Step-by-Step Solution:
Step 1: Let original cost price be C. Original selling price S1 = 1.05C.Step 2: In the alternate scenario, new cost price = 0.95C.Step 3: New selling price is S1 - 1 = 1.05C - 1.Step 4: Profit in the alternate scenario is 10%, so new selling price = 1.10 * 0.95C = 1.045C.Step 5: Equate the two expressions: 1.05C - 1 = 1.045C.Step 6: Rearrange: 1.05C - 1.045C = 1, so 0.005C = 1.Step 7: Therefore C = 1 / 0.005 = 200 rupees.

Verification / Alternative check:
With C = Rs. 200, original selling price S1 = 1.05 * 200 = Rs. 210, which is a 5% gain.Alternate cost price = 0.95 * 200 = Rs. 190.Alternate selling price = 210 - 1 = Rs. 209.Profit in alternate scenario = 209 - 190 = Rs. 19, and profit percentage = 19 / 190 * 100 = 10%, matching the condition.

Why Other Options Are Wrong:
For C = Rs. 100, Rs. 150, Rs. 250 or Rs. 300, the alternate selling price obtained by subtracting Re. 1 from the original selling price does not correspond to a 10% profit on the reduced cost price. Only C = Rs. 200 satisfies both the 5% profit in the first case and the 10% profit in the second case.

Common Pitfalls:
Some learners misapply the 5% reduction by subtracting Rs. 5 instead of 5% of C. Others forget that the second profit percentage is on the reduced cost price, not on the original. A further source of error is failing to align the two selling price expressions correctly when forming the equation. Writing each scenario separately and then equating is essential.

Final Answer:
The original cost price of the article was Rs. 200.