For a 64 kg batch of a mixture in the ratio of 9 parts A, 2 parts B, and 5 parts C, how much A is needed?

To determine how much of component A is needed in a mixture of 64 kg with the specified ratio of parts, we first need to understand the total parts represented in the mixture.

The mixture is given in the ratio of 9 parts A, 2 parts B, and 5 parts C. To find the total number of parts, we add together the parts:

9 (A) + 2 (B) + 5 (C) = 16 parts total.

Now, to find the weight of one part, we divide the total weight of the mixture by the total number of parts:

Weight of one part = Total weight / Total parts = 64 kg / 16 parts = 4 kg per part.

Next, to find out the weight of component A, we multiply the number of parts of A by the weight of one part:

Weight of A = 9 parts × 4 kg/part = 36 kg.

Thus, the amount of A needed in the 64 kg mixture is indeed 36 kg. This is why the correct answer is 36 kg.