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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

A

120

B

110

C

100

D

150

Answer

100

Explanation

Solution

Let the number of passed candidates be xx.
Then, the number of failed candidates is 120x120 - x.
The total marks of all candidates is:
120×35=4200120 \times 35 = 4200
The total marks of the passed candidates is:
x×39x \times 39
The total marks of the failed candidates is:
(120x)×15(120 - x) \times 15
The sum of the marks of passed and failed candidates should equal the total marks of all candidates:
x×39+(120x)×15=4200x \times 39 + (120 - x) \times 15 = 4200
Expanding this equation:
39x+180015x=420039x + 1800 - 15x = 4200
\Rightarrow$$24x = 2400
\Rightarrow \;$$x = \frac{2400}{24} = 100

Therefore, the number of candidates who passed is 100.