The market price of an article is 40 percent more than its cost price. A customer initially receives a discount of 28.57 percent on the market price. Next day he returns and is given one more discount equal to 12.5 percent of the cost price due to additional defects. What is the approximate overall profit or loss percentage for the seller on this article?

Introduction / Context:
This profit and loss problem involves a marked price that is higher than the cost price, followed by two successive discounts. One discount is a relatively large percentage of the marked price, and the second discount is specified as a percentage of cost price. The aim is to compute the net profit or loss percentage after both discounts are given.

Given Data / Assumptions:

• Cost price of the article = C.
• Market price (MP) = C increased by 40 percent, so MP = 1.40 * C.
• First discount on MP = 28.57 percent (approximately 2 / 7 of MP).
• Second discount given later = 12.5 percent of cost price C.
• Total discount is the sum of the first discount and this extra discount.

Concept / Approach:
To find overall gain or loss, we need the final selling price and compare it with cost price. The first discount is applied on the marked price, reducing it to a certain selling price. The extra discount is then given on top of this as a flat reduction equal to 12.5 percent of C. The combined effect gives a final selling price below or above C, which determines profit or loss percentage.

Step-by-Step Solution:
Assume cost price C = 100 units for convenience. Then market price MP = 1.40 * 100 = 140 units. First discount = 28.57 percent of MP ≈ 0.2857 * 140. Exact fraction is 2 / 7 of 140 = 40 units. So selling price after first discount = 140 - 40 = 100 units, which is equal to cost. Now an additional discount is given equal to 12.5 percent of cost price. 12.5 percent of C = 12.5 percent of 100 = 12.5 units. Final selling price = 100 - 12.5 = 87.5 units. Loss per article = cost price - final selling price = 100 - 87.5 = 12.5 units. Loss percent = 12.5 / 100 * 100 = 12.5 percent loss.

Verification / Alternative check:
Working directly from cost price: after first discount, the seller just breaks even because selling price becomes equal to cost price. Any further discount below that level will necessarily cause a loss. Since the second discount is exactly 12.5 percent of cost price, the resulting loss must also be 12.5 percent of cost price. This reasoning confirms the calculation.

Why Other Options Are Wrong:
Profit of 12.5% or 22.5%: These options assume that discounts still leave the selling price above cost, which is not possible once a further reduction below the break even point is made. Loss of 24.5%: This exaggerates the effect of the extra discount and does not match the actual arithmetic. Only a loss of 12.5 percent matches the correct computation.

Common Pitfalls:
Some candidates mistakenly think both discounts are applied on the marked price completely independently. Others ignore the fact that the second discount is specified in terms of cost price, not market price or previous selling price. Clear identification of the base values for each discount is crucial in mixed discount problems.

Final Answer:
The seller incurs an overall loss of about 12.5% on the article.