An article was sold at 12% profit. Had it purchased at 10% less and sold at Rs 5.75 more there would have been profit of 30%. Find C.P. of article?

Answer

To find the cost price (C.P.) of the article, we can follow these steps:

### Step 1: Understand the given information
- The article was sold at a profit of 12%.
- If it was purchased at 10% less and sold for Rs 5.75 more, the profit would have been 30%.

### Step 2: Set up the equations
Let the original cost price of the article be \( C \).

- Selling Price (S.P.) at 12% profit:
\[ S.P. = C + 0.12C = 1.12C \]

- If purchased at 10% less:
\[ \text{New C.P.} = C - 0.10C = 0.90C \]

- Selling Price with Rs 5.75 more:
\[ \text{New S.P.} = 1.12C + 5.75 \]

### Step 3: Set up the profit equation for the new scenario
According to the problem, if the article was sold at a 30% profit:
\[ \text{New S.P.} = \text{New C.P.} + 0.30 \times \text{New C.P.} \]
Substituting the values:
\[ 1.12C + 5.75 = 0.90C + 0.30(0.90C) \]

### Step 4: Simplify the equation
Calculating the right side:
\[ 0.30(0.90C) = 0.27C \]
Thus, the equation becomes:
\[ 1.12C + 5.75 = 0.90C + 0.27C \]
Combining like terms on the right side:
\[ 1.12C + 5.75 = 1.17C \]

### Step 5: Rearranging the equation
Now, we can rearrange the equation to isolate \( C \):
\[ 1.12C + 5.75 = 1.17C \]
Subtract \( 1.12C \) from both sides:
\[ 5.75 = 1.17C - 1.12C \]
This simplifies to:
\[ 5.75 = 0.05C \]

### Step 6: Solve for \( C \)
Now, divide both sides by 0.05 to find \( C \):
\[ C = \frac{5.75}{0.05} = 115 \]

### Final Answer
The cost price (C.P.) of the article is Rs 115.

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