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35 is the average marks obtained by 120 students. The average marks of successful candidates was 39 and that of unsuccessful candidates was 15. What is the number of successful candidates in that examination ?
- a)100
- b)110
- c)120
- d)80
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
35 is the average marks obtained by 120 students. The average marks of...
Let there be x successful candidates in the exam.
Unsuccessful candidates = 120 - x
Total score = 35 x 120
Total score is also equal to x * 39 + (120 - x) * 15
So, x = (35 * 120 - 120 * 15)/ 24 = 120 * 20 / 24 = 100
Most Upvoted Answer
35 is the average marks obtained by 120 students. The average marks of...
Understanding the Problem
To find the number of successful candidates among 120 students, given the average marks and the averages for successful and unsuccessful candidates, we can set up the problem using equations.
Information Provided
- Total students = 120
- Overall average marks = 35
- Average marks of successful candidates = 39
- Average marks of unsuccessful candidates = 15
Calculating Total Marks
- Total marks obtained by all students = Average marks × Total students
Total marks = 35 × 120 = 4200
Let’s Define Variables
- Let the number of successful candidates = x
- Therefore, the number of unsuccessful candidates = 120 - x
Setting Up the Equation
Using the averages:
- Total marks from successful candidates = 39x
- Total marks from unsuccessful candidates = 15(120 - x)
Now we can formulate the equation:
39x + 15(120 - x) = 4200
Simplifying the Equation
Expanding the equation:
39x + 1800 - 15x = 4200
Combining like terms:
24x + 1800 = 4200
Now, isolate x:
24x = 4200 - 1800
24x = 2400
x = 100
Conclusion
Thus, the number of successful candidates in the examination is 100. Hence, the correct answer is option 'A'.
To find the number of successful candidates among 120 students, given the average marks and the averages for successful and unsuccessful candidates, we can set up the problem using equations.
Information Provided
- Total students = 120
- Overall average marks = 35
- Average marks of successful candidates = 39
- Average marks of unsuccessful candidates = 15
Calculating Total Marks
- Total marks obtained by all students = Average marks × Total students
Total marks = 35 × 120 = 4200
Let’s Define Variables
- Let the number of successful candidates = x
- Therefore, the number of unsuccessful candidates = 120 - x
Setting Up the Equation
Using the averages:
- Total marks from successful candidates = 39x
- Total marks from unsuccessful candidates = 15(120 - x)
Now we can formulate the equation:
39x + 15(120 - x) = 4200
Simplifying the Equation
Expanding the equation:
39x + 1800 - 15x = 4200
Combining like terms:
24x + 1800 = 4200
Now, isolate x:
24x = 4200 - 1800
24x = 2400
x = 100
Conclusion
Thus, the number of successful candidates in the examination is 100. Hence, the correct answer is option 'A'.
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35 is the average marks obtained by 120 students. The average marks of successful candidates was 39 and that of unsuccessful candidates was 15. What is the number of successful candidates in that examination ?a)100b)110c)120d)80Correct answer is option 'A'. Can you explain this answer?
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