In a competitive examination, average marks obtained was 45 . It was later discovered that there was

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In a competitive examination, the average marks obtained was $45 .$ It was later discovered that there was some error in computerization 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

$525$

Solution

Let, the number of candidates be $x$. Then, total marks obtained by all the candidates $=45 x$

Marks reduced for $90$ candidates $=30 \times 90=2700$

Total reduced marks $=45 x-2700$.

Reduced average $=\frac{45 x-2700}{x}$

$\therefore \quad 40=\frac{45 x-2700}{x}$ or, $40 x=45 x-2700$

$\Rightarrow \quad 5 x=2700 \quad$ or, $x=540$

Standard 13

Quantitative Aptitude

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