In an event, only salesmen and guests participated.

In my opinion, more information is needed.
Can salesmen meet with other salesmen?
Can guests meet with other guests?
Can a salesman meet with a guest more than once?

For example, there could 5 salesmen and 5 guests, which means 4 salesmen (4/5 = 80%) and 2 guests (2/5 = 40%) went to the sessions.
Let the 4 salesmen be A, B, C, and D
Let the 2 guests be Y and Z

So, the meetings could have gone as follows:
AY, AY, AY, AY, AZ
BY, BZ, BY, BZ, BZ
CY, CZ, CY, CZ, CZ
DY, DZ, DY, DZ, DZ

This satisfies all parts of the question.

In this case, there are 10 attendees, and 6 of them attended sessions (6/10 = 60%)

Cheers,
Brent

Hi Brent,

Thanks for your care to answer my concern. I felt the same like you. However, the creator in his question put as follows :

Let number of salesmen = S, and guests =G

0.8 S * 5 = 0.4 G ...I do not understand the logic behind this step. Do you have any explanation that stems from the question above??

Again thanks

If S = number of salesmen, then 0.8S = number of salesmen who participated in sessions.
Each of those 0.8S salesmen had 5 sessions.
So, (5)(0.8S) = TOTAL number of sessions.

Likewise, 0.4G = number of guests who participated in sessions.
We aren't told how many sessions each of these 0.4G guests attended.
So, let k = number of sessions EACH guest attended
So, (k)(0.4G) = TOTAL number of sessions.

NOW, we can write: (5)(0.8S) = (k)(0.4G)

Thanks again Brent But is not total number of sessions = (k)(0.4G) + (5)(0.8S)...So it is still unclear to me established equation..

Can you please bear with with me and elaborate more?

Thanks in advance

The problem is that we don't have enough information (in my opinion)

I'm going to assume that each Guest attends exactly ONE session.
In other words, k = 1
Let's see what happens....

We get:
If S = number of salesmen, then 0.8S = number of salesmen who participated in sessions.
Each of those 0.8S salesmen had 5 sessions.
So, (5)(0.8S) = TOTAL number of sessions.

Likewise, 0.4G = number of guests who participated in sessions.
We aren't told how many sessions each of these 0.4G guests attended.
IF we assume that each guest attends exactly one session, then (1)(0.4G) = TOTAL number of sessions.

NOW, we can write: (5)(0.8S) = (1)(0.4G)
Simplify: 4S = 0.4G
Divide both sides by 0.4 to get: 10S = G

At this point, we have all of the info we need.
If there are G guests, and 40% of them participated in one-on-one information sessions
Then the number of GUEST session attendees = 0.4G
Since, 10S = G, we can also write: the number of GUEST session attendees = 0.4(10S) = 4S

From earlier, we also know that the number of SALESMEN session attendees = 0.8S

So, the TOTAL number of SESSION attendees 4S + 0.8S = 4.8S

Now the TOTAL number of PARTY attendees = G + S
= 10S + S
= 11S

So, the percentage of the attendees involved in the one-on-one information sessions = 4.8S/11S ≈ 43.6%

Okay, that's pretty much all the time I want to devote to this question.

Cheers,
Brent