An article was sold at 15% profit. Had it purchased at 5% more and sold at Rs 6 more there would have been profit of 10%. Find C.P. of article?

Answer

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

### Step 1: Calculate Selling Price (S.P.) at 15% profit
The selling price when sold at a 15% profit can be calculated using the formula:
\[ \text{S.P.} = \text{C.P.} + \text{Profit} = x + 0.15x = 1.15x \]

### Step 2: Calculate new C.P. and S.P. for the second scenario
If the article was purchased at 5% more, the new cost price becomes:
\[ \text{New C.P.} = x + 0.05x = 1.05x \]
If it is sold for Rs 6 more, the new selling price becomes:
\[ \text{New S.P.} = 1.15x + 6 \]

### Step 3: Set up the equation for the second scenario
According to the problem, if the article is sold at the new selling price, there would be a profit of 10%. Therefore, we can write:
\[ \text{New S.P.} = \text{New C.P.} + \text{Profit} = 1.05x + 0.10(1.05x) = 1.05x + 0.105x = 1.155x \]

### Step 4: Equate the two expressions for New S.P.
From the two expressions for New S.P., we have:
\[ 1.15x + 6 = 1.155x \]

### Step 5: Solve for \( x \)
Now, we can solve for \( x \):
\[ 1.155x - 1.15x = 6 \]
\[ 0.005x = 6 \]
\[ x = \frac{6}{0.005} = 1200 \]

### Conclusion
The cost price (C.P.) of the article is Rs 1200.