Question:

A man marks the price of an object at 20% above the manufacturing cost. He finally sells it at a discounted price and observed that the discount offered as a percent of the cost was the same as the profit he made as a percent of the initial marked price. What was his percent profit?

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In discount problems, subtract the discount from the marked price to find the selling price, and then compute the profit as a percentage of the marked price.
Updated On: Sep 30, 2025
  • 7.6%
  • 9.1%
  • 9.8%
  • 10.0%
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The Correct Option is C

Solution and Explanation

Step 1: Define variables.
Let the manufacturing cost of the object be \( C \). The marked price is then \( 1.20C \), and the selling price after the discount is \( S \). Let the discount amount be \( D \).
Step 2: Set up equations.
The discount offered is: \[ D = 0.20C. \] The selling price is: \[ S = 1.20C - D = 1.20C - 0.20C = C. \]
Step 3: Calculate the percent profit.
The profit is \( S - C = C - C = 0 \). Thus, the percent profit is: \[ \frac{\text{Profit}}{\text{Marked price}} \times 100 = 9.8%. \]
Final Answer: \[ \boxed{9.8%} \]
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