Despite giving a discount of 11.11 % on the mark-up price, profit obtained is equal to 6.66%. What is the% markup over CP?

Options

A. `14.28%`
B. `28.56%`
C. `20%`
D. `25%`

Answer

To solve the problem step by step, we will follow the information given in the question and the video transcript.

### Step 1: Define the Cost Price (CP)
Let's assume the Cost Price (CP) is 100. This will help us simplify the calculations.

### Step 2: Calculate the Selling Price (SP)
Given that the profit obtained is 6.66%, we can calculate the Selling Price (SP) using the formula:
\[ SP = CP + \text{Profit} \]
Profit is calculated as:
\[ \text{Profit} = \frac{6.66}{100} \times CP = \frac{6.66}{100} \times 100 = 6.66 \]
Thus,
\[ SP = 100 + 6.66 = 106.66 \]

### Step 3: Relate Selling Price to Marked Price (MP)
We know that a discount of 11.11% is given on the Marked Price (MP). The relationship can be expressed as:
\[ SP = MP - \text{Discount} \]
The discount can be expressed as:
\[ \text{Discount} = \frac{11.11}{100} \times MP \]
So we can write:
\[ 106.66 = MP - \frac{11.11}{100} \times MP \]
This simplifies to:
\[ 106.66 = MP \left(1 - \frac{11.11}{100}\right) = MP \left(\frac{88.89}{100}\right) \]

### Step 4: Solve for Marked Price (MP)
Now we can solve for MP:
\[ MP = \frac{106.66 \times 100}{88.89} \]
Calculating this gives:
\[ MP \approx \frac{10666}{88.89} \approx 120 \]

### Step 5: Calculate the Markup Percentage
The markup is the difference between the Marked Price (MP) and the Cost Price (CP):
\[ \text{Markup} = MP - CP = 120 - 100 = 20 \]
To find the percentage markup over the Cost Price, we use the formula:
\[ \text{Markup Percentage} = \left(\frac{\text{Markup}}{CP}\right) \times 100 \]
Substituting the values:
\[ \text{Markup Percentage} = \left(\frac{20}{100}\right) \times 100 = 20\% \]

### Final Answer
The percentage markup over the Cost Price is **20%**.

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