A man sells an article at a profit of 15%. If he had sold it for Rs 6 more, he would have gained 18%. What was the cost price of the article, in rupees?

Introduction / Context:
This classic profit and loss question compares two close selling prices for the same article, each linked to a different profit percentage. The difference between selling prices is a small fixed amount. Using this information, we build an equation to determine the unknown cost price.

Given Data / Assumptions:

• First selling price SP1 gives a profit of 15%.
• Second selling price SP2 is Rs 6 higher than SP1 and gives a profit of 18%.
• Cost price CP is the same in both cases.
• We must find CP in rupees.

Concept / Approach:
Let CP = x. Then SP1 = x * 1.15 and SP2 = x * 1.18. Given that SP2 is Rs 6 more than SP1, we write x * 1.18 = x * 1.15 + 6. Solving this simple linear equation yields the cost price. This method uses the difference between the two profit percentages and the absolute rupee difference between the selling prices.

Step-by-Step Solution:
Let CP = x rupees. First selling price SP1 = 1.15x. Second selling price SP2 = 1.18x. Given SP2 = SP1 + 6, so 1.18x = 1.15x + 6. Rearrange: 1.18x - 1.15x = 6 → 0.03x = 6. Thus x = 6 / 0.03 = 200 rupees.

Verification / Alternative check:
With CP = Rs 200, SP1 = 1.15 * 200 = Rs 230 and SP2 = 1.18 * 200 = Rs 236. The difference SP2 - SP1 = 236 - 230 = Rs 6, which matches the problem statement. Profit at SP1 = 230 - 200 = 30 rupees, which is 15% of 200. Profit at SP2 = 236 - 200 = 36 rupees, which is 18% of 200. All conditions are satisfied.

Why Other Options Are Wrong:
If CP were 100 or 150 or 250, the difference between 15% and 18% of CP would not equal 6 rupees. Only CP = 200 makes the 3% difference equal to exactly 6 rupees, because 3% of 200 is 6.

Common Pitfalls:
Many learners fail to notice that the difference between 18% and 15% is 3% and that this difference, when multiplied by CP, must equal Rs 6. Instead they might try random substitution without building a clean algebraic equation. Careless arithmetic with percentages also leads to errors.

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