A man sells an article at a profit of 35%. If he had bought it for 15% less price and sold it for Rs. 32 less, then he would have gained 40%. What is the initial cost price (in Rs) of the article?

Options

A. 250
B. 200
C. 300
D. 400

Answer

To solve the problem step by step, let's denote the initial cost price of the article as \( CP \).

### Step 1: Define the initial cost price
Let the initial cost price of the article be \( CP = 100x \).

### Step 2: Calculate the selling price with a 35% profit
If the man sells the article at a profit of 35%, the selling price \( SP \) can be calculated as:
\[ SP = CP + (35\% \text{ of } CP) = CP + 0.35 \times CP = 1.35 \times CP \]
Substituting \( CP = 100x \):
\[ SP = 1.35 \times 100x = 135x \]

### Step 3: Calculate the new cost price if it was 15% less
If he had bought the article for 15% less, the new cost price \( CP' \) would be:
\[ CP' = CP - (15\% \text{ of } CP) = CP - 0.15 \times CP = 0.85 \times CP \]
Substituting \( CP = 100x \):
\[ CP' = 0.85 \times 100x = 85x \]

### Step 4: Calculate the new selling price with a 40% profit
If he sold it for a 40% profit, the new selling price \( SP' \) would be:
\[ SP' = CP' + (40\% \text{ of } CP') = CP' + 0.40 \times CP' = 1.40 \times CP' \]
Substituting \( CP' = 85x \):
\[ SP' = 1.40 \times 85x = 119x \]

### Step 5: Set up the equation based on the information given
According to the problem, if he sold it for Rs. 32 less than the original selling price, we have:
\[ SP' = SP - 32 \]
Substituting the values we calculated:
\[ 119x = 135x - 32 \]

### Step 6: Solve for \( x \)
Rearranging the equation gives:
\[ 135x - 119x = 32 \]
\[ 16x = 32 \]
\[ x = 2 \]

### Step 7: Calculate the initial cost price
Now substituting \( x \) back to find the initial cost price:
\[ CP = 100x = 100 \times 2 = 200 \]

### Final Answer
The initial cost price of the article is **Rs. 200**.

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