After giving a discount of 33.33%, there is a loss of 11.111%. If only 10% discount is given, then what will be the profit percentage?

Options

A. 24
B. 20
C. 27
D. 25

Answer

To solve the problem step by step, we will first establish the relationship between the cost price (CP), marked price (MP), selling price (SP), and the discounts and losses involved.

### Step 1: Understand the given data
- Discount given = 33.33% (which is equivalent to 1/3)
- Loss incurred = 11.11% (which is equivalent to 1/9)
- New discount to be considered = 10% (which is equivalent to 1/10)

### Step 2: Establish the relationship between CP and MP
When a discount is given, the relationship between CP, MP, and the loss can be expressed as:
\[ \text{MP} \times (1 - \text{Discount}) = \text{CP} \times (1 - \text{Loss}) \]
Substituting the values:
\[ \text{MP} \times \left(1 - \frac{1}{3}\right) = \text{CP} \times \left(1 - \frac{1}{9}\right) \]
This simplifies to:
\[ \text{MP} \times \frac{2}{3} = \text{CP} \times \frac{8}{9} \]

### Step 3: Rearranging the equation
Rearranging the equation gives:
\[ \frac{\text{CP}}{\text{MP}} = \frac{2/3}{8/9} \]
Calculating the right side:
\[ \frac{2/3}{8/9} = \frac{2 \times 9}{3 \times 8} = \frac{18}{24} = \frac{3}{4} \]
Thus, we have:
\[ \text{CP} : \text{MP} = 3 : 4 \]

### Step 4: Assign values to CP and MP
Let:
- CP = 3x
- MP = 4x

### Step 5: Calculate the selling price (SP) with a 10% discount
With a 10% discount on the marked price:
\[ \text{SP} = \text{MP} \times (1 - 0.10) = 4x \times 0.90 = 3.6x \]

### Step 6: Calculate the profit
Profit is given by:
\[ \text{Profit} = \text{SP} - \text{CP} = 3.6x - 3x = 0.6x \]

### Step 7: Calculate the profit percentage
Profit percentage is calculated as:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 = \left(\frac{0.6x}{3x}\right) \times 100 \]
This simplifies to:
\[ \text{Profit Percentage} = \left(\frac{0.6}{3}\right) \times 100 = 20\% \]

### Final Answer
The profit percentage when a 10% discount is given is **20%**.

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