correct answer is: c) 660, 180, 210 people

Explanation

Here,
Total number of people is 1050.
Given ratio is 11\;:\;3\;:\;3\;½
Or, 11\;:\;3\;:\;\large\frac72
Let,
Number of people sit in the 1 ^st room is 11x.
Number of people sit in the 2 ^nd room is 3x.
Number of people sit in the 3 ^rd room is \large\frac{7x}{2}.
According to the question,
\left(11x+3x+\large\frac{7x}{2}\right)\normalsize=1050
\rightarrow\large\left(\frac{22x+6x+7x}{2}\right)\normalsize=1050
\rightarrow\left(22x+6x+7x\right)=\left(1050\times2\right)
\rightarrow 35x=2100
\rightarrow x=\large\frac{2100}{35}
\rightarrow x=60
So that,
Number of people sit in the 1 ^st room is 11x.
Or, \left(11\times60\right)=660 people.
Number of people sit in the 2 ^nd room is 3x.
Or, \left(3\times60\right)=180 people.
Number of people sit in the 3 ^rd room is \large\frac{7x}{2}.
Or, \large\left(\frac{7\times60}{2}\right)\normalsize=210 people.
Ans: 660 people, 180 people and 210 people will sit in each room respectively.

There’s another way to pose this same math question:

1. A total of 1050 individuals are attending training at a training center. They are to be seated in three large halls in the ratio of 11 : 3 : 3 ½. Determine the number of people allocated to each hall.
2. 1050 people are participating in training sessions at a training facility. They are instructed to occupy three large halls in the ratio of 11 : 3 : 3 ½. Calculate the number of individuals assigned to each hall.
3. At a training center, 1050 people have enrolled for training. They are to be seated in three large halls according to the ratio of 11 : 3 : 3 ½. Determine the allocation of people to each hall.