20% of marked price is equal to 30% of cost price. If no discount is given, then what will be the profit per cent ?

Options

A. 50
B. 40
C. 48
D. 45

Answer

To solve the problem step by step, we need to find the profit percentage when 20% of the marked price (MP) is equal to 30% of the cost price (CP).

### Step-by-Step Solution:

1. **Set up the equation based on the given information:**
We know that:
\[ 20\% \text{ of MP} = 30\% \text{ of CP} \]
This can be expressed mathematically as:
\[ 0.2 \times MP = 0.3 \times CP \]

2. **Rearranging the equation:**
To find the relationship between MP and CP, we can rearrange the equation:
\[ MP = \frac{0.3 \times CP}{0.2} = 1.5 \times CP \]

3. **Understanding the selling price (SP):**
Since there is no discount given, the selling price (SP) is equal to the marked price (MP):
\[ SP = MP = 1.5 \times CP \]

4. **Calculating the profit:**
Profit can be calculated as:
\[ \text{Profit} = SP - CP \]
Substituting the value of SP:
\[ \text{Profit} = (1.5 \times CP) - CP = 0.5 \times CP \]

5. **Calculating the profit percentage:**
The profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 \]
Substituting the profit we calculated:
\[ \text{Profit Percentage} = \left(\frac{0.5 \times CP}{CP}\right) \times 100 = 0.5 \times 100 = 50\% \]

### Final Answer:
The profit percentage is **50%**.