First you need to work out what 10% of $15 is. You can do this on a calculator by converting the fraction into decimal which is 0.10 and then multiplying 15 by 0.10:
15 x 0.10 = 1.50
Then since the owner increased the price by 10%, we simply do 15 + 1.50 which gives us 16.50
Therefore the owner charges $16.50 for 1kg of sugar