If `60%` discount is offered on the marked price and selling price becomes equal to cost price then what was the `%` mark up?

Options

A. 100
B. 250
C. 150
D. 40

Answer

To solve the problem step by step, we will break down the information given and derive the necessary calculations to find the percentage markup.

### Step 1: Understand the relationship between Marked Price, Selling Price, and Cost Price
- Let the marked price (MP) be denoted as \( MP \).
- A discount of \( 60\% \) is offered on the marked price. Therefore, the selling price (SP) can be calculated as:
\[ SP = MP - (60\% \text{ of } MP) = MP \times (1 - 0.6) = 0.4 \times MP \]

### Step 2: Set up the equation based on the given information
- According to the problem, the selling price becomes equal to the cost price (CP):
\[ SP = CP \]
Substituting the expression for SP:
\[ 0.4 \times MP = CP \]

### Step 3: Express CP in terms of MP
- From the equation \( 0.4 \times MP = CP \), we can express CP as:
\[ CP = 0.4 \times MP \]

### Step 4: Find the ratio of Marked Price to Cost Price
- We can rearrange the equation to find the ratio of marked price to cost price:
\[ \frac{MP}{CP} = \frac{MP}{0.4 \times MP} = \frac{1}{0.4} = \frac{10}{4} = \frac{5}{2} \]

### Step 5: Assign values to MP and CP
- Let’s assign values based on the ratio:
- Let \( CP = 2k \)
- Then, \( MP = 5k \)

### Step 6: Calculate the markup percentage
- The markup is defined as the difference between the marked price and the cost price:
\[ \text{Markup} = MP - CP = 5k - 2k = 3k \]
- The markup percentage is calculated as:
\[ \text{Markup Percentage} = \left( \frac{\text{Markup}}{CP} \right) \times 100 = \left( \frac{3k}{2k} \right) \times 100 \]
- Simplifying this gives:
\[ \text{Markup Percentage} = \frac{3}{2} \times 100 = 150\% \]

### Conclusion
- The percentage markup is \( 150\% \).