A trader bought a number of articles for RS.1200. Ten were damaged and he sold each of the rest at RS. 2 more than what he paid for it, thus clearing a profit of RS.60 on the whole transaction. Find the number of articles he bought.

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Define Variables
Let \( x \) be the total number of articles the trader bought. The total cost of the articles is given as RS. 1200.

### Step 2: Calculate Cost per Article
The cost per article \( a \) can be calculated as:
\[ a = \frac{1200}{x} \]

### Step 3: Determine Remaining Articles
Since 10 articles were damaged, the number of articles sold is:
\[ x - 10 \]

### Step 4: Selling Price per Article
The selling price per article is RS. 2 more than the cost price, which can be expressed as:
\[ \text{Selling Price} = a + 2 = \frac{1200}{x} + 2 \]

### Step 5: Total Selling Price
The total selling price for the remaining articles is:
\[ \text{Total Selling Price} = (x - 10) \left( \frac{1200}{x} + 2 \right) \]

### Step 6: Profit Calculation
The trader made a profit of RS. 60 on the whole transaction. Therefore, we can set up the equation:
\[ \text{Total Selling Price} = \text{Total Cost} + \text{Profit} \]
\[ (x - 10) \left( \frac{1200}{x} + 2 \right) = 1200 + 60 \]
\[ (x - 10) \left( \frac{1200}{x} + 2 \right) = 1260 \]

### Step 7: Expand the Equation
Expanding the left-hand side:
\[ (x - 10) \left( \frac{1200}{x} + 2 \right) = (x - 10) \cdot \frac{1200}{x} + (x - 10) \cdot 2 \]
\[ = \frac{1200x - 12000}{x} + 2x - 20 \]
Combining the terms gives:
\[ \frac{1200x - 12000 + 2x^2 - 20x}{x} = 1260 \]

### Step 8: Clear the Denominator
Multiplying through by \( x \) to eliminate the fraction:
\[ 1200x - 12000 + 2x^2 - 20x = 1260x \]

### Step 9: Rearranging the Equation
Rearranging gives:
\[ 2x^2 - 1260x + 1200x - 12000 + 20 = 0 \]
\[ 2x^2 - 80x - 12000 = 0 \]

### Step 10: Simplifying the Equation
Dividing the entire equation by 2:
\[ x^2 - 40x - 6000 = 0 \]

### Step 11: Factoring the Quadratic
Factoring the quadratic:
\[ (x - 100)(x + 60) = 0 \]

### Step 12: Finding the Roots
Setting each factor to zero gives:
\[ x - 100 = 0 \quad \text{or} \quad x + 60 = 0 \]
Thus:
\[ x = 100 \quad \text{or} \quad x = -60 \]

### Step 13: Conclusion
Since the number of articles cannot be negative, we conclude:
\[ \text{The number of articles he bought is } 100. \]