After allowing a discount of 12% on the marked price, a shopkeeper still gains 21%. The marked price is above the cost price by

Options

A. `25%`
B. `30%`
C. `37.5%`
D. `42.5%`

Answer

To solve the problem step by step, we need to establish the relationship between the marked price (MP), cost price (CP), and the discount and profit percentages given in the question.

### Step 1: Understand the given information
- Discount = 12%
- Gain (Profit) = 21%

### Step 2: Define the relationships
Let:
- Cost Price (CP) = 100 (for simplicity)
- Marked Price (MP) = x

### Step 3: Calculate the Selling Price (SP)
The Selling Price (SP) after a discount of 12% on the marked price can be calculated as follows:
\[ SP = MP - (12\% \text{ of } MP) \]
\[ SP = x - 0.12x = 0.88x \]

### Step 4: Calculate the Selling Price based on Profit
Since the shopkeeper gains 21% on the cost price, we can express the Selling Price as:
\[ SP = CP + (21\% \text{ of } CP) \]
\[ SP = 100 + 0.21 \times 100 = 121 \]

### Step 5: Set the two expressions for Selling Price equal
From Step 3 and Step 4, we have:
\[ 0.88x = 121 \]

### Step 6: Solve for the Marked Price (MP)
Now, we can solve for x (the marked price):
\[ x = \frac{121}{0.88} \]
Calculating this gives:
\[ x = 137.5 \]

### Step 7: Find the difference between Marked Price and Cost Price
Now we need to find how much the marked price is above the cost price:
\[ MP - CP = 137.5 - 100 = 37.5 \]

### Conclusion
The marked price is above the cost price by **37.5**.

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