a) 760, 180, 210 people

b) 660, 180, 200 people

c) 660, 180, 210 people

d) 600, 180, 210 people

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:

**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.****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.****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.**