When an article is sold at 75% of certain selling price, there is a loss of 20%. Calculate profit percent when the same article is sold at 125% of the certain selling price?

Options

A. A)`33(1)/(3)%`
B. B)`22(2)/(9)%`
C. C)`30%`
D. D)`32(1)/(2)%`

Answer

To solve the problem step by step, we will follow the given information and calculate the required values.

### Step 1: Define the Selling Price (SP) and Cost Price (CP)
Let the certain selling price (SP) be 100 units.

### Step 2: Calculate the Selling Price when sold at 75% of SP
When the article is sold at 75% of the certain selling price:
\[ SP_1 = 75\% \text{ of } 100 = 75 \text{ units} \]

### Step 3: Determine the Loss Percentage
It is given that there is a loss of 20%. This means the selling price is less than the cost price.

Using the formula for loss:
\[ \text{Loss} = CP - SP \]
Given that the loss is 20%, we can express this as:
\[ \text{Loss} = 20\% \text{ of } CP = \frac{20}{100} \times CP = 0.2 \times CP \]

### Step 4: Set up the equation for Cost Price (CP)
From the previous information, we can write:
\[ CP - SP_1 = 0.2 \times CP \]
Substituting \( SP_1 = 75 \):
\[ CP - 75 = 0.2 \times CP \]
Rearranging gives:
\[ CP - 0.2 \times CP = 75 \]
\[ 0.8 \times CP = 75 \]
Thus, we can find the cost price:
\[ CP = \frac{75}{0.8} = 93.75 \text{ units} \]

### Step 5: Calculate the Selling Price when sold at 125% of SP
Now, we need to find the selling price when the article is sold at 125% of the certain selling price:
\[ SP_2 = 125\% \text{ of } 100 = 125 \text{ units} \]

### Step 6: Determine the Profit
Now, we can calculate the profit when sold at \( SP_2 \):
\[ \text{Profit} = SP_2 - CP \]
Substituting the values:
\[ \text{Profit} = 125 - 93.75 = 31.25 \text{ units} \]

### Step 7: Calculate the Profit Percentage
To find the profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{31.25}{93.75} \right) \times 100 \]
Calculating the fraction:
\[ \text{Profit Percentage} = \left( \frac{31.25}{93.75} \right) \times 100 = \frac{1}{3} \times 100 = 33.33\% \]

### Final Answer
The profit percentage when the article is sold at 125% of the certain selling price is:
\[ \text{Profit Percentage} = 33 \frac{1}{3} \% \]

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