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 steps:

### Step 1: Define Variables
Let \( n \) be the total number of articles bought by the trader. The cost of all articles is given as Rs. 1200. Therefore, the cost price per article \( p \) can be expressed as:
\[ p = \frac{1200}{n} \]

### Step 2: Determine the Number of Articles Sold
Since 10 articles were damaged, the number of articles sold is:
\[ n - 10 \]

### Step 3: Selling Price Calculation
The trader sells each of the remaining articles at Rs. 2 more than the cost price. Thus, the selling price per article becomes:
\[ p + 2 = \frac{1200}{n} + 2 \]

### Step 4: Total Selling Price
The total selling price for the articles sold is given by:
\[ \text{Total Selling Price} = (n - 10) \left( \frac{1200}{n} + 2 \right) \]

### Step 5: Profit Calculation
The total profit made on the transaction is Rs. 60. Therefore, the total selling price can also be expressed as:
\[ \text{Total Selling Price} = \text{Cost Price} + \text{Profit} = 1200 + 60 = 1260 \]

### Step 6: Set Up the Equation
Now, we can set up the equation:
\[ (n - 10) \left( \frac{1200}{n} + 2 \right) = 1260 \]

### Step 7: Expand the Equation
Expanding the left side:
\[ (n - 10) \left( \frac{1200}{n} + 2 \right) = (n - 10) \cdot \frac{1200}{n} + (n - 10) \cdot 2 \]
This simplifies to:
\[ \frac{1200(n - 10)}{n} + 2(n - 10) = 1260 \]

### Step 8: Clear the Fraction
Multiply through by \( n \) to eliminate the fraction:
\[ 1200(n - 10) + 2n(n - 10) = 1260n \]

### Step 9: Simplify the Equation
Expanding gives:
\[ 1200n - 12000 + 2n^2 - 20n = 1260n \]
Rearranging the equation:
\[ 2n^2 + (1200 - 20 - 1260)n - 12000 = 0 \]
This simplifies to:
\[ 2n^2 - 80n - 12000 = 0 \]

### Step 10: Divide by 2
Dividing the entire equation by 2:
\[ n^2 - 40n - 6000 = 0 \]

### Step 11: Factor the Quadratic Equation
We need to factor the quadratic equation. We look for two numbers that multiply to \(-6000\) and add to \(-40\). The numbers are \(-100\) and \(60\):
\[ (n - 100)(n + 60) = 0 \]

### Step 12: Solve for \( n \)
Setting each factor to zero gives:
\[ n - 100 = 0 \quad \Rightarrow \quad n = 100 \]
\[ n + 60 = 0 \quad \Rightarrow \quad n = -60 \quad (\text{not valid since } n \text{ cannot be negative}) \]

### Conclusion
Thus, the number of articles the trader bought is:
\[ \boxed{100} \]