After giving a discount of 25%, a shopkeeper earns 40% profit. Marked price is what percent more than the cost price?

Options

A. `80%`
B. `75%`
C. `86.67%`
D. `85%`

Answer

To solve the problem step by step, we need to find out what percentage more the marked price is than the cost price, given the discount and profit percentages.

### Step 1: Understand the given information
- Discount = 25%
- Profit = 40%

### Step 2: Define the variables
Let:
- Cost Price (CP) = 100 (for ease of calculation)
- Marked Price (MP) = ?
- Selling Price (SP) = CP + Profit = 100 + 40% of 100 = 140

### Step 3: Calculate the Selling Price after discount
Since the shopkeeper gives a discount of 25% on the Marked Price, we can express the Selling Price in terms of the Marked Price:
- Selling Price (SP) = Marked Price (MP) - Discount on MP
- Discount on MP = 25% of MP = 0.25 * MP
- Therefore, SP = MP - 0.25 * MP = 0.75 * MP

### Step 4: Set up the equation
From Step 2, we know that SP = 140. Now we can set up the equation:
\[ 0.75 \cdot MP = 140 \]

### Step 5: Solve for Marked Price (MP)
To find MP, we rearrange the equation:
\[ MP = \frac{140}{0.75} \]
\[ MP = \frac{140 \times 100}{75} = \frac{14000}{75} = 186.67 \]

### Step 6: Calculate the percentage more of MP than CP
Now we need to find out how much more the Marked Price is than the Cost Price:
- Difference = MP - CP = 186.67 - 100 = 86.67
- Percentage more = \(\frac{Difference}{CP} \times 100\)
\[ \text{Percentage more} = \frac{86.67}{100} \times 100 = 86.67\% \]

### Final Answer
The Marked Price is 86.67% more than the Cost Price.

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