If an article is sold at a gain of 6% instead of a loss of 6%, the seller receives Rs. 6 more in selling price. What is the cost price of the article in rupees?

Introduction / Context:
This is a classic profit and loss question where replacing a loss with a gain of the same percentage changes the selling price by a known rupee amount. The key observation is that the difference between a 6% gain and a 6% loss is a total change of 12% of the cost price. Knowing the rupee difference in selling price allows us to compute the cost price directly.

Given Data / Assumptions:

• If sold at 6% loss, there is one selling price.
• If sold at 6% gain, there is another selling price.
• Difference between these two selling prices = Rs. 6.
• Let cost price (CP) of the article be C rupees.

Concept / Approach:
At a loss of 6%, selling price SP1 = 0.94C. At a gain of 6%, selling price SP2 = 1.06C. The difference SP2 − SP1 equals 1.06C − 0.94C = 0.12C, which is 12% of C. The problem states that this difference equals Rs. 6. Therefore, 0.12C = 6, from which we can solve for C directly, giving the cost price.

Step-by-Step Solution:
Let cost price of the article be C rupees. Selling price at 6% loss: SP1 = C * (1 − 6 / 100) = 0.94C. Selling price at 6% gain: SP2 = C * (1 + 6 / 100) = 1.06C. Difference between the two selling prices: SP2 − SP1 = 1.06C − 0.94C. SP2 − SP1 = 0.12C. Given that this difference equals Rs. 6. So, 0.12C = 6. Therefore, C = 6 / 0.12. Compute 6 / 0.12 = 50. Thus, the cost price of the article is Rs. 50.

Verification / Alternative check:
Check with C = Rs. 50. At 6% loss, SP1 = 0.94 * 50 = Rs. 47. At 6% gain, SP2 = 1.06 * 50 = Rs. 53. Difference SP2 − SP1 = 53 − 47 = Rs. 6, which matches the given condition. Hence C = 50 is fully consistent with the problem statement.

Why Other Options Are Wrong:
18, 36, 42 and 60: For each of these cost prices, the difference between 6% gain and 6% loss would be 12% of the chosen value. In each case, 12% of that value is not equal to 6 rupees. For example, for 60, 12% of 60 is 7.2, not 6.

Common Pitfalls:
A common error is to treat the difference in percentages (6% and −6%) as 6% instead of 12%. The gain and loss act in opposite directions, so the total change in percentage is 6% + 6% = 12%. Another mistake is to misinterpret “gain instead of loss” and set up only one selling price expression. Always write both selling price formulas and subtract them to form the correct equation.

Final Answer:
The cost price of the article is Rs. 50.