Question

In a public show, 75% of the seats were filled. If there were 600 seats in the hall, how many seats were vacant?
A) 150
B) 200
C) 300
D) 250

Answer 1

Hint: In this problem use formula of converting number into percentage of total number by using the formula of percentage which is given below:
$\dfrac{{{\text{number for which percentage is to be calculated}}}}{{{\text{total number}}}} \times 100$.

Complete step-by-step answer:
We have given the total number of seats available are 600 seats and the percentage of seats which are filled are 75%. We have to find the number of vacant seats.
We have to find the number of vacant seats that are available to sit.
So, let the number of seats filled be $x$.
It is given that $75\% $ of the seats are filled and there are total $600$ seats in the show, then substitute the values of total number and percentage and total number in the above formula and solve for $x$.
Number of filled seats$ = 75\% {\text{ of }}600$
Number of filled seats $ = \dfrac{{75}}{{100}} \times 600$
Number of filled seats $ = 450$
So, the total number of seats which are filled are 450 out of 600 seats.
Now, to calculate the vacant seats from 600, we will subtract the number of filled seats from the total number of seats.
Mathematically, total vacant seats $ = 600 - 450 = 150$
So, the number of vacant seats in a show are 150 seats.

Therefore, the option A is correct.

Note: We can also find the number of vacant seats by alternate method.
It is given that $75\% $ of seats are filled then it means that $25\% $ of seats are vacant out of $600$ seats.
Then the number of vacant seats is given as:
Number of vacant seats $ = 25\% {\text{ of }}600$
Number of vacant seats$ = \dfrac{{25}}{{100}} \times 600$
Number of vacant seats $ = 150$
Hence, there are $150$ vacant seats out of $600$ seats.