Question:
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
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
Updated On: Jan 30, 2025
- 120
- 110
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The Correct Option is C
Solution and Explanation
Let the number of passed candidates be \(x\).
Then, the number of failed candidates is \(120 - x\).
The total marks of all candidates is:
\(120 \times 35 = 4200\)
The total marks of the passed candidates is:
\(x \times 39\)
The total marks of the failed candidates is:
\((120 - x) \times 15\)
The sum of the marks of passed and failed candidates should equal the total marks of all candidates:
\(x \times 39 + (120 - x) \times 15 = 4200\)
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.
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