A candy distributor needs to mix 10% a fat content chocolate with 40% fat content chocolate to create 200 kg of a 16% fat content chocolate how many kilograms of each kind of chocolate must they use

I like to use an X diagram to solve problems like this. The constituent percentages are on the left, the desired mix is in the middle and the numbers on the diagonals are the difference between the mix and the constituent.

The numbers 6 and 24 here represent the ratio of 40% to 10% chocolate. That 6:24 ratio can be reduced to 1:4. The sum of those ratio units is 1+4 = 5, so each must represent (200 kg) / 5 = 40 kg of chocolate.

The mix must consist of

40 kg of 40% fat chocolate

160 kg of 10% fat chocolate