Question
Mathematics Question on Average
The average of marks obtained by 120 candidates was 35. If the average of the passed candidates was 39 and that of the failed candidates was 15, then the number of those candidates who passed the examination, was
120
110
100
150
100
Solution
Let the number of passed candidates be x.
Then, the number of failed candidates is 120−x.
The total marks of all candidates is:
120×35=4200
The total marks of the passed candidates is:
x×39
The total marks of the failed candidates is:
(120−x)×15
The sum of the marks of passed and failed candidates should equal the total marks of all candidates:
x×39+(120−x)×15=4200
Expanding this equation:
39x+1800−15x=4200
\Rightarrow$$24x = 2400
\Rightarrow \;$$x = \frac{2400}{24} = 100
Therefore, the number of candidates who passed is 100.