A man bought an article and sold it at a gain of 5%. If he had bought it at 5% less and sold it for Rs. 1 less, he would have made a profit of 10%. The Cost Price(C.P.) of an article was

Options

A. Rs. 150
B. Rs. 200
C. Rs. 250
D. Rs. 350

Answer

To solve the problem step by step, let's denote the Cost Price (C.P.) of the article as \( x \).

### Step 1: Calculate the Selling Price (S.P.) with a 5% gain
The selling price when the article is sold at a gain of 5% can be calculated as:
\[ \text{S.P.} = \text{C.P.} + \text{Gain} \]
Where Gain = 5% of C.P. = \( 0.05x \).

Thus,
\[ \text{S.P.} = x + 0.05x = 1.05x \]

### Step 2: Calculate the new C.P. and S.P. when bought at 5% less
If the man had bought the article at 5% less, the new C.P. would be:
\[ \text{New C.P.} = x - 0.05x = 0.95x \]

### Step 3: Calculate the S.P. for a 10% gain based on the new C.P.
If he sold it for Rs. 1 less and made a profit of 10%, the new S.P. can be calculated as:
\[ \text{New S.P.} = \text{New C.P.} + \text{Profit} \]
Where Profit = 10% of New C.P. = \( 0.10 \times 0.95x = 0.095x \).

Thus,
\[ \text{New S.P.} = 0.95x + 0.095x = 1.045x \]

### Step 4: Set up the equation based on the Rs. 1 less condition
According to the problem, the new S.P. is Rs. 1 less than the original S.P.:
\[ 1.05x - 1 = 1.045x \]

### Step 5: Solve for \( x \)
Now, we will solve the equation:
\[ 1.05x - 1.045x = 1 \]
\[ 0.005x = 1 \]
\[ x = \frac{1}{0.005} = 200 \]

### Conclusion
The Cost Price (C.P.) of the article is Rs. 200.

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