A man sells an article at 10% profit. Ifhe buys it for 10% less than its value & sells it for 3 more than its firs selling price he wil gain 25% Find the cost price of the article.

Options

A. Rs 120
B. Rs 125
C. Rs 100
D. Rs 128

Answer

To solve the problem step by step, let's denote the following:

- Let the cost price (CP) of the article be \( x \).
- The selling price (SP) at a 10% profit will then be \( SP_1 = x + 0.1x = 1.1x \).

### Step 1: Determine the cost price when bought at 10% less
If he buys the article for 10% less than its value, the new cost price (CP') will be:
\[ CP' = x - 0.1x = 0.9x \]

### Step 2: Selling price when sold for 3 more than the first selling price
According to the problem, he sells it for 3 more than the first selling price:
\[ SP_2 = SP_1 + 3 = 1.1x + 3 \]

### Step 3: Determine the profit when selling at SP2
He gains a profit of 25% on the new cost price (CP'):
\[ SP_2 = CP' + 0.25 \times CP' = 1.25 \times CP' = 1.25 \times 0.9x = 1.125x \]

### Step 4: Set the two expressions for SP2 equal to each other
Now we can set the two expressions for \( SP_2 \) equal to each other:
\[ 1.1x + 3 = 1.125x \]

### Step 5: Solve for x
Rearranging the equation gives:
\[ 3 = 1.125x - 1.1x \]
\[ 3 = 0.025x \]
\[ x = \frac{3}{0.025} = 120 \]

### Conclusion
The cost price of the article is \( \text{Rs. } 120 \).