A man sells an article at 5% profit. If he had bought it at 5% less and sold if for Rs. 1 less, he would have gained 10%. Find the cost price.'

Options

A. 100
B. 150
C. 200
D. 250

Answer

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

### Step 1: Calculate Selling Price (SP) at 5% profit
When the man sells the article at a 5% profit, the selling price (SP) can be calculated as:
\[ SP = CP + 5\% \text{ of } CP = x + 0.05x = 1.05x \]

### Step 2: Calculate the new cost price
If he had bought the article at 5% less, the new cost price (CP') would be:
\[ CP' = CP - 5\% \text{ of } CP = x - 0.05x = 0.95x \]

### Step 3: Calculate the new selling price
If he sells it for Rs. 1 less than the original selling price, the new selling price (SP') would be:
\[ SP' = SP - 1 = 1.05x - 1 \]

### Step 4: Set up the equation for 10% profit
According to the problem, if he had bought it at the new cost price and sold it for the new selling price, he would have gained 10%. Therefore, we can express this as:
\[ SP' = CP' + 10\% \text{ of } CP' = 0.95x + 0.10 \times 0.95x = 0.95x + 0.095x = 1.045x \]

### Step 5: Equate the two expressions for SP'
Now we can set the two expressions for the new selling price equal to each other:
\[ 1.05x - 1 = 1.045x \]

### Step 6: Solve for x
Now, we will solve for \( x \):
\[ 1.05x - 1.045x = 1 \]
\[ 0.005x = 1 \]
\[ x = \frac{1}{0.005} = 200 \]

### Conclusion
The cost price of the article is \( \text{Rs. } 200 \).

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