Given:
- The trader bought a number of articles for ₹900.
- Five articles were found to be damaged.
- He sold each of the remaining articles at ₹2 more.
- He made a profit of ₹80 in the whole transaction.

To Find:
The number of articles he bought.

Assumptions:
- The cost price of each article is the same.
- The selling price of each undamaged article is ₹2 more than the cost price.

Let's Solve the Problem:

Step 1: Calculate the cost price per article
- The total cost of all the articles is ₹900.
- Since the cost price of each article is the same, let's assume it to be 'x'.
- Therefore, the equation becomes: 5x (for 5 damaged articles) + (total number of undamaged articles * x) = ₹900.
- Simplifying the equation: 5x + (total number of undamaged articles * x) = ₹900.
- Combining like terms: (5 + total number of undamaged articles) * x = ₹900.
- We can rewrite this equation as: (total number of undamaged articles + 5) * x = ₹900.

Step 2: Calculate the selling price per undamaged article
- The selling price per undamaged article is ₹2 more than the cost price.
- Therefore, the selling price per undamaged article is (x + ₹2).

Step 3: Calculate the total selling price of undamaged articles
- The total selling price of undamaged articles can be calculated as follows:
- Total selling price = (total number of undamaged articles * selling price per undamaged article).
- Total selling price = (total number of undamaged articles * (x + ₹2)).

Step 4: Calculate the profit
- The profit can be calculated by subtracting the total cost price from the total selling price.
- Profit = Total selling price - Total cost price.
- Profit = [(total number of undamaged articles * (x + ₹2)) + ₹80] - ₹900.

Step 5: Solve the equations
- Now, we have two equations:
- Equation 1: (total number of undamaged articles + 5) * x = ₹900.
- Equation 2: [(total number of undamaged articles * (x + ₹2)) + ₹80] - ₹900 = 0.

Step 6: Find the number of articles
- Solve the above two equations simultaneously to find the value of 'x' and the total number of undamaged articles.

Conclusion:
- By solving the equations, we can find the number of articles the trader bought.