There is some concept that is confusing me here. In this problem:
Based on statistical data in a company, communication path between two persons consumes 5% of each person’s time (during a 8-hour work day).
so my confusion is should I plugin the same 5% for wasted time in communication during a month? So for example if there are 6 communication paths does it mean 30% wasted time in one month ? How about two months? is it still 30%? So if there are 5 people and 10 communication paths, does it mean 50% of their time is used up in communicating?
Assuming the communication paths don't overlap or otherwise interfere with each other, the percentage will stay at 5%. What you're not taking into account is that while it is true that with 6 paths, 6 times the amount of time is consumed communicating, there is also 6 times as much available time for the people to do other things.
However, if there is a network of three or more people (i.e. there is an overlap), then a greater percentage of time is spent communicating, since each person has to talk to more than one other person.
You can see this if you draw out the network as a polygon with some (or all) of its diagonals drawn in to represent communication between people. The number of lines emanating from each vertex is the number of communication paths for that person, and in that case the percentages to add up.
In summary, increasing the time or number of paths (but making sure each person only communicates with one other person) does not increase the percentage, but increasing the number of connections per person does.
So, in your question about 5 people and 10 communication paths, which can be represented by a pentagon with 5 people. Since each vertex (person) has 4 lines connecting to other people, the percentage is cumulative and each person spends $4\cdot5\%=20\%$ of their time communicating.