A trader marks his good such that he can make 32% profit after giving 12% discount. However a customer available 20% discount instead of 12%. What is the new profit percentage of trader?

Options

A. `20%`
B. `44%`
C. `30%`
D. `28.8%`

Answer

To solve the problem step by step, we need to find the new profit percentage of the trader when the discount changes from 12% to 20%.

### Step 1: Determine the relationship between Mark Price (MP), Cost Price (CP), Profit Percentage, and Discount Percentage.

The formula for the relationship is given by:
\[ \frac{MP}{CP} = \frac{100 + \text{Profit Percentage}}{100 - \text{Discount Percentage}} \]

### Step 2: Calculate the initial ratio of MP to CP with the given profit and discount percentages.

Given:
- Profit Percentage = 32%
- Discount Percentage = 12%

Substituting these values into the formula:
\[ \frac{MP}{CP} = \frac{100 + 32}{100 - 12} = \frac{132}{88} \]

### Step 3: Simplify the ratio.

Now, simplify the fraction:
\[ \frac{132}{88} = \frac{3}{2} \]

### Step 4: Set up the equation for the new discount.

Now, we need to find the new profit percentage (let's denote it as \(P'\)) when the discount is changed to 20%. The formula becomes:
\[ \frac{MP}{CP} = \frac{100 + P'}{100 - 20} \]

### Step 5: Substitute the known ratio into the new equation.

We already know that:
\[ \frac{MP}{CP} = \frac{3}{2} \]
So we can set up the equation:
\[ \frac{100 + P'}{80} = \frac{3}{2} \]

### Step 6: Cross-multiply to solve for \(P'\).

Cross-multiplying gives us:
\[ 2(100 + P') = 3 \times 80 \]
\[ 2(100 + P') = 240 \]

### Step 7: Expand and isolate \(P'\).

Expanding the left side:
\[ 200 + 2P' = 240 \]

Now, isolate \(P'\):
\[ 2P' = 240 - 200 \]
\[ 2P' = 40 \]
\[ P' = \frac{40}{2} = 20 \]

### Step 8: Conclusion

The new profit percentage of the trader is:
\[ \text{Profit Percentage} = 20\% \]