7/9 of the people present in a hall are sitting in 9/13 of the chairs ...
Given:
7/9 of the people present in a hall are sitting in 9/13 of the chairs available and the rest are standing, and there are 28 empty chairs.
To Find:
Number of chairs that would have been still empty if everyone in the hall was sitting.
Solution:
Let's assume the total number of people present in the hall is 'x', and the total number of chairs available is 'y'.
According to the given condition,
7/9 of the people present are sitting, and the rest are standing.
Therefore, the number of people sitting = 7/9 * x
And, the number of people standing = 2/9 * x (since 7/9 + 2/9 = 1)
Also, 9/13 of the chairs available are occupied by the people sitting.
Therefore, the number of chairs occupied by the people sitting = 9/13 * y
Now, let's calculate the number of empty chairs in the hall:
Total number of chairs - Number of chairs occupied by people sitting = Number of empty chairs
y - (9/13 * y) = 4/13 * y
We are given that there are 28 empty chairs, so we can write:
4/13 * y = 28
y = 91
Hence, the total number of chairs available in the hall is 91.
Now, let's calculate the number of chairs that would have been still empty if everyone in the hall was sitting:
Number of chairs occupied by people sitting + Number of chairs occupied by people standing = Total number of chairs
9/13 * y + 2/9 * x = y
Substituting the values of y and 7/9 * x (since 7/9 of the people present are sitting) in the above equation, we get:
9/13 * 91 + 2/9 * (7/9 * x) = 91
Simplifying this equation, we get:
x = 70
So, the total number of people present in the hall is 70.
If everyone in the hall was sitting, then the total number of chairs occupied would be:
7/9 * 91 = 70
Therefore, the number of empty chairs would be:
91 - 70 = 21
However, we are given that there are 28 empty chairs, which means that some people are still standing.
Let's calculate the number of people standing:
Number of people standing = Total number of people present - Number of people sitting
= 70 - 7/9 * 70
= 70 - 560/9
= 2/9 * 70
= 20
Therefore, the number of chairs that would have been still empty if everyone in the hall was sitting is:
Total number of empty chairs + Number of chairs occupied by people standing
= 28 + 20
= 48
Hence, the correct answer is option 'D' (10).
7/9 of the people present in a hall are sitting in 9/13 of the chairs ...
Let the number of people be x and number of the chair be y.
Number of available chair = y × (9/13) = 9y/13
Number of empty chair = y - (9y/13) = 4y/13
Given, Number of empty chairs = 28
According to the question
4y/13 = 28
y = 28 × (13/4) = 91
Total number of chairs = 91
Number of chairs in which people are sitting = 91 - 28 = 63
Number of people who sit = x × (7/9) = 7x/9
According to the question
7x/9 = 63
x = 63 × (9/7) = 81
Total number of people are = 81
Chairs would have been still empty if everyone in the hall was sitting = 91 - 81 = 10
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