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The average mark of 15 students in a CSAT test is 50. If the average mark of the first eight students is 47 and that of the last eight students is 55, then what will be the marks of the 8th student?
- a)56
- b)66
- c)70
- d)86
Correct answer is option 'B'. Can you explain this answer??
The average mark of 15 students in a CSAT test is 50. If the average mark of the first eight students is 47 and that of the last eight students is 55, then what will be the marks of the 8th student?
a)
56
b)
66
c)
70
d)
86
|
Nandini Saha answered |
Total Marks Calculation
To find the marks of the 8th student, we need to first calculate the total marks of all students and the marks of the first and last groups of students.
- The average mark of 15 students is 50.
- Thus, the total marks for all 15 students = 15 * 50 = 750.
First Eight Students' Marks
- The average mark of the first eight students is 47.
- Therefore, the total marks for the first eight students = 8 * 47 = 376.
Last Eight Students' Marks
- The average mark of the last eight students is 55.
- Thus, the total marks for the last eight students = 8 * 55 = 440.
Overlap Calculation
- Note that the 8th student is included in both the first and the last group. Hence, we need to adjust for this overlap:
- Total marks of both groups combined = 376 + 440 - marks of the 8th student.
Setting Up the Equation
- We have the total marks from all students as 750:
- 376 + 440 - marks of the 8th student = 750.
Solving for the 8th Student's Marks
- Simplifying the equation gives:
- 816 - marks of the 8th student = 750.
- Therefore, marks of the 8th student = 816 - 750 = 66.
Conclusion
- The marks of the 8th student is 66, which corresponds to option 'B'.
To find the marks of the 8th student, we need to first calculate the total marks of all students and the marks of the first and last groups of students.
- The average mark of 15 students is 50.
- Thus, the total marks for all 15 students = 15 * 50 = 750.
First Eight Students' Marks
- The average mark of the first eight students is 47.
- Therefore, the total marks for the first eight students = 8 * 47 = 376.
Last Eight Students' Marks
- The average mark of the last eight students is 55.
- Thus, the total marks for the last eight students = 8 * 55 = 440.
Overlap Calculation
- Note that the 8th student is included in both the first and the last group. Hence, we need to adjust for this overlap:
- Total marks of both groups combined = 376 + 440 - marks of the 8th student.
Setting Up the Equation
- We have the total marks from all students as 750:
- 376 + 440 - marks of the 8th student = 750.
Solving for the 8th Student's Marks
- Simplifying the equation gives:
- 816 - marks of the 8th student = 750.
- Therefore, marks of the 8th student = 816 - 750 = 66.
Conclusion
- The marks of the 8th student is 66, which corresponds to option 'B'.
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