if the discount given is equal to 25 percent of the selling price and the sale gives the trader a rfit of 50/3 percent when calculated on his selling price by what percent did he mark up the cost price before offering the discount a)50% b)65% c)55% d)60%

Let the cost price be \( C \) and the marked price be \( M \).

Given:

1. The discount is 25% of the selling price.
2. The trader gains a profit of \( \frac{50}{3} \)% on the selling price.

### Step-by-Step Analysis

1. Let the selling price be \( S \).  
   Since the discount is 25% of the selling price:

   \[
   M = S + 0.25S = 1.25S
   \]

2. The profit is \( \frac{50}{3} \)% of the selling price \( S \):

   \[
   \text{Profit} = \frac{50}{3}\% \text{ of } S = \frac{50}{300} \times S = \frac{S}{6}
   \]

3. The cost price \( C \) can be represented as:

   \[
   C = S - \text{Profit} = S - \frac{S}{6} = \frac{5S}{6}
   \]

4. Now, the markup percentage is calculated as:

   \[
   \text{Markup Percentage} = \frac{M - C}{C} \times 100
   \]

   Substituting the values:

   \[
   \text{Markup Percentage} = \frac{1.25S - \frac{5S}{6}}{\frac{5S}{6}} \times 100
   \]

   Simplifying the expression:

   \[
   \text{Markup Percentage} = \frac{\frac{1.25S \times 6}{6} - \frac{5S}{6}}{\frac{5S}{6}} \times 100 = \frac{\frac{7.5S - 5S}{6}}{\frac{5S}{6}} \times 100 = \frac{\frac{2.5S}{6}}{\frac{5S}{6}} \times 100 = \frac{2.5}{5} \times 100 = 0.5 \times 100 = 50\%
   \]

### Final Answer

The correct answer is:

**(a) 50%**

Would you like more details or have any other questions?

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Here are 5 related questions you might be interested in:

1. How do you calculate profit percentages when given cost and selling prices?
2. What are the different types of discounts and how do they affect pricing strategies?
3. How do you find the marked price given a percentage discount and cost price?
4. What are the steps to convert fractions into percentages in profit or discount problems?
5. How does markup differ from margin in percentage calculations?

**Tip:** Understanding percentage calculations is crucial for solving most profit and loss problems. Always break down the steps and solve systematically.

Learn how to calculate markup percentage based on profit and discount percentages. This problem involves understanding profit and loss calculations, including markup percentage on cost price. Suitable for high school students.

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