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The average of marks obtained by 120 candidates was 35. If the average of marks of passed candidates was 39 and that of failed candidates was 15, the number of candidates who passed the examination is:
- a)80
- b)110
- c)100
- d)70
Correct answer is option 'C'. Can you explain this answer?
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The average of marks obtained by 120 candidates was 35. If the average...
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The average of marks obtained by 120 candidates was 35. If the average...
To find the number of candidates who passed the examination, we need to determine the number of candidates who failed the examination and then subtract it from the total number of candidates.
Given:
- Total number of candidates = 120
- Average marks of all candidates = 35
- Average marks of passed candidates = 39
- Average marks of failed candidates = 15
Let's solve this problem step by step:
Step 1: Find the total marks obtained by all candidates.
The total marks obtained by all candidates can be calculated by multiplying the average marks by the number of candidates.
Total marks = Average marks * Number of candidates
Total marks = 35 * 120 = 4200
Step 2: Find the total marks obtained by the passed candidates.
The total marks obtained by the passed candidates can be calculated by multiplying the average marks of passed candidates by the number of passed candidates.
Total marks of passed candidates = Average marks of passed candidates * Number of passed candidates
Total marks of passed candidates = 39 * Number of passed candidates
Step 3: Find the total marks obtained by the failed candidates.
The total marks obtained by the failed candidates can be calculated by multiplying the average marks of failed candidates by the number of failed candidates.
Total marks of failed candidates = Average marks of failed candidates * Number of failed candidates
Total marks of failed candidates = 15 * Number of failed candidates
Step 4: Set up an equation using the total marks obtained by all candidates.
Since the total marks obtained by all candidates is equal to the sum of the total marks obtained by the passed candidates and the total marks obtained by the failed candidates, we can set up the following equation:
Total marks = Total marks of passed candidates + Total marks of failed candidates
4200 = 39 * Number of passed candidates + 15 * Number of failed candidates
Step 5: Use the equation to solve for the number of passed candidates.
Substitute the given values into the equation and solve for the number of passed candidates:
4200 = 39 * Number of passed candidates + 15 * Number of failed candidates
4200 = 39 * Number of passed candidates + 15 * (120 - Number of passed candidates)
4200 = 39 * Number of passed candidates + 1800 - 15 * Number of passed candidates
4200 - 1800 = 39 * Number of passed candidates - 15 * Number of passed candidates
2400 = 24 * Number of passed candidates
Number of passed candidates = 2400 / 24
Number of passed candidates = 100
Therefore, the number of candidates who passed the examination is 100.
Given:
- Total number of candidates = 120
- Average marks of all candidates = 35
- Average marks of passed candidates = 39
- Average marks of failed candidates = 15
Let's solve this problem step by step:
Step 1: Find the total marks obtained by all candidates.
The total marks obtained by all candidates can be calculated by multiplying the average marks by the number of candidates.
Total marks = Average marks * Number of candidates
Total marks = 35 * 120 = 4200
Step 2: Find the total marks obtained by the passed candidates.
The total marks obtained by the passed candidates can be calculated by multiplying the average marks of passed candidates by the number of passed candidates.
Total marks of passed candidates = Average marks of passed candidates * Number of passed candidates
Total marks of passed candidates = 39 * Number of passed candidates
Step 3: Find the total marks obtained by the failed candidates.
The total marks obtained by the failed candidates can be calculated by multiplying the average marks of failed candidates by the number of failed candidates.
Total marks of failed candidates = Average marks of failed candidates * Number of failed candidates
Total marks of failed candidates = 15 * Number of failed candidates
Step 4: Set up an equation using the total marks obtained by all candidates.
Since the total marks obtained by all candidates is equal to the sum of the total marks obtained by the passed candidates and the total marks obtained by the failed candidates, we can set up the following equation:
Total marks = Total marks of passed candidates + Total marks of failed candidates
4200 = 39 * Number of passed candidates + 15 * Number of failed candidates
Step 5: Use the equation to solve for the number of passed candidates.
Substitute the given values into the equation and solve for the number of passed candidates:
4200 = 39 * Number of passed candidates + 15 * Number of failed candidates
4200 = 39 * Number of passed candidates + 15 * (120 - Number of passed candidates)
4200 = 39 * Number of passed candidates + 1800 - 15 * Number of passed candidates
4200 - 1800 = 39 * Number of passed candidates - 15 * Number of passed candidates
2400 = 24 * Number of passed candidates
Number of passed candidates = 2400 / 24
Number of passed candidates = 100
Therefore, the number of candidates who passed the examination is 100.
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The average of marks obtained by 120 candidates was 35. If the average of marks of passed candidates was 39 and that of failed candidates was 15, the number of candidates who passed the examination is:a)80b)110c)100d)70Correct answer is option 'C'. Can you explain this answer?
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