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

Correct option is (c) 540

Let the number of candidates = x.

The given average = 45.

Then the total of the marks = 45x .

The change in marks for 90 candidates = 80 − 50 = 30 for each.

The total = 90 × 30 = 2700

So the total marks now is 45x − 2700.

The new average of marks = 40.

Then total = 40x.

By the given condition,

45x − 2700 = 40x

5x = 2700

x = 540

So the number of candidates = 540.