How much percent above the cost price should a shopkeeper mark his goods so as to earn a profit of 32% after allowing a discount of 12% on the marked price ?

Options

A. `50%`
B. `40%`
C. `60%`
D. `45%`

Answer

To solve the problem of how much percent above the cost price a shopkeeper should mark his goods to earn a profit of 32% after allowing a discount of 12% on the marked price, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Cost Price, Marked Price, and Selling Price**:
- Let the Cost Price (CP) be represented as \( CP \).
- The Selling Price (SP) after allowing a discount on the Marked Price (MP) can be expressed as:
\[ SP = MP \times \left(1 - \frac{\text{Discount}}{100}\right) \]
- In this case, the discount is 12%, so:
\[ SP = MP \times \left(1 - 0.12\right) = MP \times 0.88 \]

2. **Express Selling Price in Terms of Cost Price**:
- The shopkeeper wants to earn a profit of 32%, which means:
\[ SP = CP \times \left(1 + \frac{\text{Profit}}{100}\right) = CP \times 1.32 \]

3. **Set the Two Expressions for Selling Price Equal**:
- We have two expressions for SP:
\[ MP \times 0.88 = CP \times 1.32 \]

4. **Rearranging to Find the Marked Price**:
- Rearranging the equation gives:
\[ MP = \frac{CP \times 1.32}{0.88} \]

5. **Calculate the Ratio of Marked Price to Cost Price**:
- To find how much percent above the cost price the marked price is, we can express the ratio of \( MP \) to \( CP \):
\[ \frac{MP}{CP} = \frac{1.32}{0.88} \]

6. **Simplify the Ratio**:
- Calculate \( \frac{1.32}{0.88} \):
\[ \frac{1.32}{0.88} = \frac{132}{88} = \frac{33}{22} = \frac{3}{2} \]
- This means that \( MP = 1.5 \times CP \).

7. **Calculate the Percentage Increase**:
- The increase in price from CP to MP is:
\[ MP - CP = 1.5 \times CP - CP = 0.5 \times CP \]
- To find the percentage increase over the cost price:
\[ \text{Percentage Increase} = \left(\frac{MP - CP}{CP}\right) \times 100 = \left(\frac{0.5 \times CP}{CP}\right) \times 100 = 50\% \]

### Final Answer:
The shopkeeper should mark his goods **50% above the cost price**.