Marked price is 25% more than the selling price of the product and the profit earned on selling is also 25%. If the difference between profit and the difference between cost price and marked price is Rs 200, then find the cost price of the product?

Options

A. Rs 500
B. Rs 640
C. Rs 600
D. Rs 700

Answer

To solve the problem step by step, we will define the variables and use the information given in the question.

### Step 1: Define Variables
Let the Cost Price (CP) be \( x \).

### Step 2: Calculate Selling Price (SP)
According to the question, the Selling Price (SP) is 25% more than the Cost Price. Therefore:
\[ SP = CP + 0.25 \times CP = 1.25 \times CP = 1.25x \]

### Step 3: Calculate Marked Price (MP)
The Marked Price (MP) is also given to be 25% more than the Selling Price. Thus:
\[ MP = SP + 0.25 \times SP = 1.25 \times SP = 1.25 \times (1.25x) = 1.5625x \]

### Step 4: Calculate Profit
The profit earned on selling is given as 25% of the Cost Price. Therefore:
\[ \text{Profit} = SP - CP = 1.25x - x = 0.25x \]

### Step 5: Set Up the Equation
According to the question, the difference between the profit and the difference between the Cost Price and the Marked Price is Rs 200. We can express this as:
\[ \text{Profit} - (MP - CP) = 200 \]
Substituting the values we found:
\[ 0.25x - (1.5625x - x) = 200 \]
This simplifies to:
\[ 0.25x - 0.5625x = 200 \]
\[ -0.3125x = 200 \]

### Step 6: Solve for Cost Price (CP)
Now, we can solve for \( x \):
\[ x = \frac{200}{-0.3125} = -640 \]
Since we are looking for a positive cost price, we take the absolute value:
\[ CP = 640 \]

### Conclusion
The Cost Price of the product is Rs 640.

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