Question

In a competitive examination, the average marks obtained was 45. It was later discovered that there was some error in computerisation and the marks of 90 candidates had to be changed from 80 to 50 and the average came down to 40 marks. The total number of candidates who appeared in examination is
A. 520
B. 550
C. 540
D. 560

Answer 1

Hint: Let the number of candidates be $x$. First, calculate the sum of total marks. Then, find the change in the number of marks according to the given condition. Subtract it from the previous sum of marks and equate it to the new sum of total marks and find the value of $x$.

Complete step-by-step answer:
We are given that the average mark was 45.
Let the number of students be $x$.
Then, the total marks of the candidates will be \[45x\].
We are given that there is a change of marks from 80 to 50 for 90 candidates.
This implies, there is a change of 30 marks for 1 student.
To find the number of marks that are extra in total marks is $90\left( {30} \right) = 2700$
Then, the total number of marks of the students is $45x - 2700$
We are also given that the new average is 40
Then, total sum of marks will be $40x$
Hence, we have
$
   \Rightarrow 45x - 2700 = 40x \\
   \Rightarrow 5x = 2700 \\
$
Divide both sides by 5
$x = 540$
Therefore, there are 540 candidates who appeared in the competitive exam.
Hence, option C is correct.

Note: Average of a data is given as $\dfrac{{{\text{Sum of observations}}}}{{{\text{Number of observations}}}}$. Then, the sum of observations will be calculated by multiplying the average with the number of observations.