Two boxes, A and B, have the capacity of holding 85 and 68 units of an article respectively. However, these articles have to be first packed into uniformly sized smaller packets that fit into the boxes. What is the maximum number of units that should be put into each of these packets such that both boxes A and B are filled to their full capacity?

Correct option is C

Given:

Capacity of box A = 85 units

Capacity of box B = 68 units

We need to find the maximum number of units that should be put into each packet such that both boxes A and B are filled to their full capacity.

Solution:

First, divide 85 by 68:

​$$85 \div 68 = 1 \quad \text{(quotient)} \quad \text{remainder} = 85 - 68 \times 1 = 17$$​​

Now, divide 68 by 17:

​$$68 \div 17 = 4 \quad \text{(quotient)} \quad \text{remainder} = 0$$​

Since the remainder is 0, the GCD is the last non-zero remainder, which is 17.

The maximum number of units that should be put into each packet is 17.