A dealer sold an article at a loss of 6%. Had he sold it for Rs 64 more, he would have made a profit of 10%. What was the cost price of the article?

Introduction / Context:
This question tests your ability to connect two different selling situations for the same article, one with a loss and one with a profit, and to use the difference in selling price to deduce the cost price. It is a standard type of profit and loss problem where two percentage conditions are given along with an absolute difference in rupees.

Given Data / Assumptions:

• The article is first sold at a loss of 6%.
• If it had been sold for Rs 64 more, there would have been a profit of 10%.
• We need to find the cost price of the article.
• Cost price is the same in both hypothetical selling situations.

Concept / Approach:
Let cost price be CP. Selling price at 6% loss is CP * (1 - 6 / 100) = 0.94 * CP. Selling price at 10% profit is CP * (1 + 10 / 100) = 1.10 * CP. The difference between these two selling prices is given as Rs 64. So we set 1.10 * CP - 0.94 * CP = 64 and solve for CP.

Step-by-Step Solution:
Let CP be the cost price of the article.SP1 at 6% loss = 0.94 * CP.SP2 at 10% profit = 1.10 * CP.Given SP2 is Rs 64 more than SP1, so SP2 - SP1 = 64.Therefore 1.10 * CP - 0.94 * CP = 64.0.16 * CP = 64.CP = 64 / 0.16 = 400.So the cost price of the article is Rs 400.

Verification / Alternative check:
Take CP = Rs 400. At 6% loss, SP1 = 400 * 0.94 = Rs 376. At 10% profit, SP2 = 400 * 1.10 = Rs 440. The difference SP2 - SP1 = 440 - 376 = Rs 64, which exactly matches the condition in the question. This confirms that the cost price of Rs 400 is correct.

Why Other Options Are Wrong:
If CP were Rs 200, the difference between 10% profit price and 6% loss price would be 0.16 * 200 = Rs 32, not Rs 64. Similarly, CP of Rs 164 or Rs 464 would also yield incorrect differences. Only CP = Rs 400 results in a difference of Rs 64 between the two selling scenarios.

Common Pitfalls:
One common mistake is to forget that both percentages are applied to the same cost price and instead try to use the difference between 10% and 6% directly on some selling price. Another error is in simple arithmetic with decimals and percentages. Carefully writing the equations with multipliers makes the structure clear and avoids confusion.

Final Answer:
The cost price of the article is Rs 400.