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 appeared in the examination is:

• A. 520
• B. 550
• C. 540
• D. 525
• E. None of these

Answer 1

The correct option is C 540

Let, the number of candidates be x. Then, total marks obtained by all the candidates = 45x.
Marks reduced for 90 candidates = $30\times 90=2700$
Total reduced marks $=45x-2700$
Reduced average $=\frac{45x-2700}{x}$
$\therefore 40=\frac{45x-2700}{x}or,40x=45x-2700$
$\Rightarrow 5x=2700$ or, $x=540$