The average of marks obtained by 120 candidates in a certain examination is 35. If the average marks of passed candidates is 39 and that of the failed candidates is 15, what is the number of candidates who passed the examination?
Show Hint
When two groups have different averages, use total \(=\) (avg\(_1\)\(\times\)size\(_1\)) \(+\) (avg\(_2\)\(\times\)size\(_2\)), or set up a weighted-average equation and solve for the group size.
- 90
- 85
- 100
- 120
The Correct Option is C
Solution and Explanation
Step 1: Convert averages to total marks.
Overall average \(=35\) for \(120\) candidates \(\Rightarrow\) total marks \(=120\times 35=4200\).
Step 2: Let the number of passed candidates be \(p\).
Then failed candidates \(=120-p\).
Total marks \(=\) (passed total) \(+\) (failed total)
\[ 39p + 15(120-p) = 4200. \]
Step 3: Solve for \(p\).
\[ 39p + 1800 - 15p = 4200 \Rightarrow 24p = 2400 \Rightarrow p = 100. \] \[ \boxed{100} \]
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