The average weight of 10 men is increased by 1.5 kg when one of them, who weighs 70 kg is replaced by a new man. The weight of the new man is:

The average of the men is solely changing due to the change in the weight of the person being replaced. No other person in the group is coming in or going out. 
This means the change in the average of 1.5kg, which is calculated over 10 men, is solely due to the heavier person coming in. 
The change in average is 1.5kg, which means the change in the total amount of weight will be 15 kg.

This means the new man coming in is 15kgs heavier than the old man. The old man weighs 70kgs, this means the new man will weight 85kgs.