Question

In an examination, the average was found to be 50 marks. After deducting computerization errors the marks of the 100 candidates had to be changed from 90 to 60 each and the average camr down to 45 marks. The total number of candidates who took the examination were

Answer 1

Answer:

Initially, average marks = 50

Let the total number of candidates = x

ATQ,

50 × x= 45 × x+ 100 (90 – 60)

50x– 45x= 100 × 30

5x= 3000

x= 600

So, the total number of candidates = 600

Answer 2

The total number of candidates who took the examination were 600

Solution:

Let the number of students be "x"

In an examination, the average was found to be 50 marks

The average is given as:

$Average = \frac{sum\ of\ marks}{total\ students}\\\\50 = \frac{sum\ of\ marks}{x}\\\\sum\ of\ marks = 50x$

After deducting computerization errors the marks of the 100 candidates had to be changed from 90 to 60 each and the average came down to 45 marks

Therefore, according to this condition,

$\frac{50x - 100(90 - 60)}{x} = 45\\\\50x - 100 \times 30 = 45x\\\\50x - 3000 = 45x\\\\5x = 3000\\\\x = 600$

Thus the total number of candidates who took the examination were 600

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