In this question, we are given that a man sells an article for Rs. 2700 and incurs a loss of 10%.

Let`s calculate the cost price of the article:

If the selling price is 90% (100% - 10%) of the cost price, then Rs. 2700 represents 90% of the cost price.

Thus, the cost price of the article can be calculated by dividing Rs. 2700 by 90%:

Cost price = Rs. 2700 / 0.9 = Rs. 3000.

Now, we are asked to find the gain percentage when the article is sold for Rs. 3600.

To calculate this, we need to find the profit made on selling the article for Rs. 3600.

Profit = Selling price - Cost price = Rs. 3600 - Rs. 3000 = Rs. 600.

To find the gain percentage, we use the formula:

Gain percentage = (Profit / Cost price) * 100

= (600 / 3000) * 100

= 20%.

Therefore, the correct answer is option 3, which represents a gain percentage of 20%.