An article was sold at 10% profit. Had it purchased at 5% less and sold at Rs 110 less there would have been profit of 10%. Find C.P. of article?

Answer

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

### Step 1: Determine the Selling Price (S.P.) at 10% profit
The article is sold at a 10% profit. Therefore, the Selling Price (S.P.) can be calculated as:
\[ \text{S.P.} = \text{C.P.} + 10\% \text{ of C.P.} = x + 0.1x = 1.1x \]

### Step 2: Determine the new Cost Price when purchased at 5% less
If the article was purchased at 5% less, the new Cost Price becomes:
\[ \text{New C.P.} = x - 5\% \text{ of } x = x - 0.05x = 0.95x \]

### Step 3: Determine the Selling Price when sold at Rs 110 less
If the article is sold at Rs 110 less than the original selling price, the new Selling Price becomes:
\[ \text{New S.P.} = \text{Original S.P.} - 110 = 1.1x - 110 \]

### Step 4: Set up the equation for 10% profit on the new Cost Price
According to the problem, if the article is sold at the new Selling Price, there would be a profit of 10% on the new Cost Price. Therefore, we can write:
\[ \text{New S.P.} = \text{New C.P.} + 10\% \text{ of New C.P.} \]
Substituting the values we have:
\[ 1.1x - 110 = 0.95x + 0.1(0.95x) \]
\[ 1.1x - 110 = 0.95x + 0.095x \]
\[ 1.1x - 110 = 1.045x \]

### Step 5: Solve for x
Now, we can solve for \( x \):
\[ 1.1x - 1.045x = 110 \]
\[ 0.055x = 110 \]
\[ x = \frac{110}{0.055} = 2000 \]

### Conclusion
The Cost Price (C.P.) of the article is \( \text{Rs } 2000 \).