The average weight of 8 women increases by 2.5 kg when a new woman replaces one of them weighing 65 kg. Find the weight of the new woman.

85

Average weight of 8 women - x

1 woman was added and 1 was replaced

Average weight of 8 women after replacement - x + 2.5

That means the new woman who came had at least that amount of weight that the replaced woman had apart from that she had some more weight which eventually resulted in an increase in the average of all the women. 

So, weight of new woman can be calculated as: 

65 (weight of old woman) + 2.5 x 8 (extra weight that resulted in an increase) = weight of new woman

65 + 20 = 85 years