After giving a discount of 20% there is a profit of 20%. If 5% discount is given, then what will be the profit percentage?

Options

A. 40.5
B. 42.5
C. 47.5
D. 52.5

Answer

To solve the problem step-by-step, we will first establish the relationship between the cost price (CP), selling price (SP), and marked price (MP) based on the discounts and profits given in the question.

### Step 1: Establish the relationship with the given discount and profit
Given:
- A discount of 20% results in a profit of 20%.

Let:
- CP = Cost Price
- MP = Marked Price
- SP = Selling Price

From the information given:
- After a 20% discount, the selling price (SP) can be calculated as:
\[ SP = MP - (20\% \text{ of } MP) = MP \times (1 - 0.20) = 0.80 \times MP \]

- The profit of 20% means:
\[ SP = CP + (20\% \text{ of } CP) = CP \times (1 + 0.20) = 1.20 \times CP \]

### Step 2: Set up the equation
Since both expressions equal SP, we can set them equal to each other:
\[ 0.80 \times MP = 1.20 \times CP \]

### Step 3: Rearranging the equation
Rearranging gives us:
\[ \frac{MP}{CP} = \frac{1.20}{0.80} = \frac{12}{8} = \frac{3}{2} \]

This means that the ratio of Marked Price to Cost Price is 3:2.

### Step 4: Assign values based on the ratio
Let:
- CP = 200 (for simplicity)
- MP = 300 (based on the ratio 3:2)

### Step 5: Calculate Selling Price with a 5% discount
If a 5% discount is given on the marked price:
\[ \text{Discount} = 5\% \text{ of } MP = 0.05 \times 300 = 15 \]
Thus, the new Selling Price (SP) becomes:
\[ SP = MP - \text{Discount} = 300 - 15 = 285 \]

### Step 6: Calculate Profit
Now, we can calculate the profit:
\[ \text{Profit} = SP - CP = 285 - 200 = 85 \]

### Step 7: Calculate Profit Percentage
Finally, the profit percentage is calculated as:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{85}{200} \right) \times 100 = 42.5\% \]

### Final Answer
The profit percentage when a 5% discount is given is **42.5%**.

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