Question

The cost price of an article is 64% of the marked price. Calculate the percent gain after allowing a discount of 12%?

• A. 87.5 %
• B. 33.33 %
• C. 52.5 %
• D. 37.5 %
• E. 62.5 %

Hint:

For percentage problems involving CP, MP, and SP, it's often easiest to assume the Marked Price as 100 to avoid fractions.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Profit is the difference between Selling Price and Cost Price, calculated as a percentage of Cost Price.
Step 2: Key Formula or Approach:
Profit % \( = \frac{SP - CP}{CP} \cdot 100 \). Assume MP = 100.
Step 3: Detailed Explanation:
Let Marked Price (MP) \( = 100 \).
Cost Price (CP) \( = 64% \) of 100 \( = 64 \).
Discount \( = 12% \) of 100 \( = 12 \).
Selling Price (SP) \( = MP - \text{Discount} = 100 - 12 = 88 \).
Profit \( = 88 - 64 = 24 \).
Profit % \( = (24 / 64) \cdot 100 = (3 / 8) \cdot 100 \).
Since \( 1/8 = 12.5% \), \( 3/8 = 3 \cdot 12.5 = 37.5% \).
Step 4: Final Answer:
The percent gain is 37.5 %.