Question

What will be the profit percentage on selling an article at a certain price if there is 30% loss on selling the article at \(\frac{4}{5}\) of the selling price?

• A. 20%
• B. 25%
• C. 35%
• D. \(12\frac{1}{2}\)%

Hint:

In such problems, assume the Cost Price (CP) to be a convenient number like 100. Then \(SP' = 70\). Since \(SP' = (4/5)SP\), then \(70 = (4/5)SP\), which gives \(SP = 87.5\). Comparing SP (87.5) to CP (100) shows a 12.5% loss.

Answer 1

The Correct Option is D

Step 1: Define variables. Let CP be the Cost Price and SP be the original Selling Price. Let the new selling price be \( SP' = \frac{4}{5} \times SP \).

Step 2: Formulate an equation based on the loss condition. At \(SP'\), there is a 30% loss. This means the item was sold for 70% of its cost price. \[ SP' = CP \times (1 - 0.30) = 0.70 \times CP \]

Step 3: Relate the original selling price (SP) to the cost price (CP). We have two expressions for \(SP'\), so we can equate them: \[ \frac{4}{5} SP = 0.70 \times CP \] Now, solve for SP in terms of CP: \[ SP = \frac{5}{4} \times 0.70 \times CP = 1.25 \times 0.70 \times CP = 0.875 \times CP \]

Step 4: Determine the profit or loss at the original selling price. The original selling price is 87.5% of the cost price. Since \(SP<CP\), it is a loss. Loss = CP - SP = \( CP - 0.875 \times CP = 0.125 \times CP \). The loss percentage is 12.5% or \(12\frac{1}{2}%\). Note: The question asks for a profit percentage, which is contradictory to the result. This suggests a typo in the question's values. However, the numerical value matches option D.