$$\frac{6}{11}$$​ of the people present in a hall are sitting in $$\frac{9}{14}$$​ of the chairs available, and the rest are standing. If there are 30 empty chairs, how many people in the hall are standing?

Correct option is C

Given:
Fraction of people sitting =$$\frac{6}{11}$$​ of the total people.
Fraction of chairs occupied = $$\frac{9}{14}$$​ of the total chairs.
Empty chairs = 30.
Solution:
Let P be the total number of people in the hall.

Let C be the total number of chairs available.
People sitting occupy chairs: $$\frac{6}{11}P$$​​
These occupy$$\frac{9}{14}C$$​ of the chairs.
Thus:
​$$\frac{6}{11}P = \frac{9}{14}C$$​​
Empty chairs = Total chairs - Occupied chairs.
​$$C - \frac{9}{14}C = 30$$​​

​$$\frac{5}{14}C = 30$$​

C = $$30 \times \frac{14}{5}$$​

C = 84 
From Step 2:
​$$\frac{6}{11}P = \frac{9}{14} \times 84$$​​

​$$\frac{6}{11}P = 54$$​​

P =$$54 \times \frac{11}{6}$$​

P = 99 
People sitting: $$\frac{6}{11} \times 99 = 54$$​​

People standing: Total people - Sitting people.
= 99 - 54 = 45 
The number of people standing in the hall is 45.