After giving a discount of `35%`, there is a loss of `7.14%`. If only `20%` discount is given, then what will be the profit percentage?

Options

A. `11.11`
B. `12.5`
C. `14.28`
D. `16.66`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
We know that after giving a discount of 35%, there is a loss of 7.14%. We need to find the profit percentage when a discount of 20% is given.

### Step 2: Establish the relationship between Cost Price (CP), Marked Price (MP), and Selling Price (SP)
1. Let the Marked Price (MP) be \( x \).
2. A discount of 35% means the Selling Price (SP) after discount is:
\[ SP = MP \times (1 - \text{Discount Percentage}) = x \times (1 - 0.35) = x \times 0.65 \]
3. Given that there is a loss of 7.14%, we can express this as:
\[ SP = CP \times (1 - \text{Loss Percentage}) = CP \times (1 - 0.0714) = CP \times 0.9286 \]

### Step 3: Set up the equation
From the above, we have:
\[ x \times 0.65 = CP \times 0.9286 \]
This can be rearranged to find the ratio of CP to MP:
\[ \frac{CP}{MP} = \frac{0.65}{0.9286} \]

### Step 4: Calculate the ratio
Calculating the right-hand side:
\[ \frac{CP}{MP} = \frac{65}{92.86} \approx \frac{65 \times 100}{92.86 \times 100} = \frac{6500}{9286} \approx \frac{7}{10} \]
Thus, we can conclude:
\[ CP : MP = 7 : 10 \]

### Step 5: Assign values to CP and MP
Let:
- Cost Price (CP) = \( 7x \)
- Marked Price (MP) = \( 10x \)

### Step 6: Calculate Selling Price (SP) with a 20% discount
1. A discount of 20% means:
\[ SP = MP \times (1 - 0.20) = 10x \times 0.80 = 8x \]

### Step 7: Calculate Profit
Profit is given by:
\[ \text{Profit} = SP - CP = 8x - 7x = x \]

### Step 8: Calculate Profit Percentage
Profit percentage is calculated as:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{x}{7x} \right) \times 100 = \frac{1}{7} \times 100 \approx 14.28\% \]

### Final Answer
The profit percentage when a discount of 20% is given is approximately **14.28%**.

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