Question & Answer
QUESTION

In a theatre, 280 came out to watch a movie, but the seats were only 200. What is the percentage error?

ANSWER Verified Verified
Hint: For solving this problem, the total number of visitors that can be accommodated in the theatre is equal to the total number of seats. By using this methodology, we calculate the excess number of visitors coming to the theatre to watch a movie. After this, apply the percentage formula to get the answer.

Complete Step-by-Step solution:
According to the problem statement, we are given that the total number of seats available in a theatre for watching a movie is equal to 200. But, at one time 280 people come together to watch a single movie in the same theatre. So, the number of people which can be accommodated is 280 – 200 = 80.
Therefore, the number of people inside the theatre is 80.
Now, to obtain the percentage we divide the excess amount of people with the people accommodated inside the theatre.
$\dfrac{80}{200}=\dfrac{2}{5}$
After multiplying it by hundred, we obtain the percentage error.
$\dfrac{2}{5}\times 100=40%$
Therefore, the percentage error at the theatre is 40%.

Note: The key concept involved in solving this problem is the knowledge of percentage for a given data. Once we know the excess quantity, we can easily evaluate the percentage by dividing it with the initial given quantity. This is a direct question and can be easily solved by students.