An article is sold at 20% loss. If the article is sold Rs 100 more than the first S.P. then he get 15%o loss find out the selling price of the article when the profit is 25%.

Options

A. Rs 2400
B. Rs 2100
C. Rs 2500
D. Rs 5000

Answer

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

### Step 1: Define Variables
Let the cost price (CP) of the article be \( x \).

### Step 2: Calculate the Selling Price at 20% Loss
If the article is sold at a 20% loss, the selling price (SP1) can be calculated as:
\[ SP1 = CP - (20\% \text{ of } CP) = x - 0.2x = 0.8x \]

### Step 3: Calculate the Selling Price at 15% Loss
According to the problem, if the article is sold for Rs 100 more than the first selling price, the loss becomes 15%. Therefore, the new selling price (SP2) is:
\[ SP2 = SP1 + 100 = 0.8x + 100 \]
At 15% loss, the selling price can also be expressed as:
\[ SP2 = CP - (15\% \text{ of } CP) = x - 0.15x = 0.85x \]

### Step 4: Set Up the Equation
Now, we can set the two expressions for SP2 equal to each other:
\[ 0.8x + 100 = 0.85x \]

### Step 5: Solve for x
Rearranging the equation gives:
\[ 100 = 0.85x - 0.8x \]
\[ 100 = 0.05x \]
\[ x = \frac{100}{0.05} = 2000 \]

### Step 6: Calculate the Selling Price for 25% Profit
Now that we have the cost price \( x = 2000 \), we can find the selling price when there is a 25% profit:
\[ SP = CP + (25\% \text{ of } CP) = x + 0.25x = 1.25x \]
\[ SP = 1.25 \times 2000 = 2500 \]

### Final Answer
The selling price of the article when the profit is 25% is **Rs 2500**.

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