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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?
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The average mark of 15 students in a CSAT test is 50. If the average m...
Find the sum of the total marks of first 8 students. similarly for the last 8 students and then find the diff from the total marks.
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The average mark of 15 students in a CSAT test is 50. If the average m...
Given:
- Total number of students = 15
- Average mark of all 15 students = 50
- Average mark of the first 8 students = 47
- Average mark of the last 8 students = 55
To find:
- Marks of the 8th student
Approach:
1. We know that the average is calculated by dividing the sum of all values by the total number of values.
2. We can use the formula: Average = Sum/Number of values
3. Let's assume the sum of marks of all 15 students is S.
4. We can write two equations using the given information:
- (Sum of marks of the first 8 students)/8 = 47 ---> Equation 1
- (Sum of marks of the last 8 students)/8 = 55 ---> Equation 2
5. From equation 1, we can write the sum of marks of the first 8 students as 8 * 47 = 376.
6. From equation 2, we can write the sum of marks of the last 8 students as 8 * 55 = 440.
7. Now, let's find the sum of marks of the remaining students (9th to 15th) using the formula:
- Sum of marks of remaining students = Sum of marks of all 15 students - Sum of marks of the first 8 students - Sum of marks of the last 8 students
- Sum of marks of remaining students = S - 376 - 440
- Sum of marks of remaining students = S - 816
8. We know that the average mark of all 15 students is 50. So, using the formula: Average = Sum/Number of values, we can write:
- S/15 = 50
- S = 750
9. Substituting the value of S in equation 8, we get:
- Sum of marks of remaining students = 750 - 816
- Sum of marks of remaining students = -66
10. Since we know the sum of marks of the remaining students, we can find the average mark of the remaining students using the formula: Average = Sum/Number of values.
- Average mark of the remaining students = (-66)/(15 - 8)
- Average mark of the remaining students = (-66)/7
- Average mark of the remaining students = -9.43 (approx)
11. Now, since we have the average mark of the remaining students, we can find the marks of the 8th student by multiplying the average mark of the remaining students by 7 and subtracting it from the sum of marks of the first 8 students.
- Marks of the 8th student = (Average mark of the first 8 students) * 8 - (Average mark of the remaining students) * 7
- Marks of the 8th student = 47 * 8 - (-9.43) * 7
- Marks of the 8th student = 376 + 66 (approx)
- Marks of the 8th student = 442 (approx)
Conclusion:
The marks of the 8th student will be approximately 442. Therefore, the correct answer is option B)
- Total number of students = 15
- Average mark of all 15 students = 50
- Average mark of the first 8 students = 47
- Average mark of the last 8 students = 55
To find:
- Marks of the 8th student
Approach:
1. We know that the average is calculated by dividing the sum of all values by the total number of values.
2. We can use the formula: Average = Sum/Number of values
3. Let's assume the sum of marks of all 15 students is S.
4. We can write two equations using the given information:
- (Sum of marks of the first 8 students)/8 = 47 ---> Equation 1
- (Sum of marks of the last 8 students)/8 = 55 ---> Equation 2
5. From equation 1, we can write the sum of marks of the first 8 students as 8 * 47 = 376.
6. From equation 2, we can write the sum of marks of the last 8 students as 8 * 55 = 440.
7. Now, let's find the sum of marks of the remaining students (9th to 15th) using the formula:
- Sum of marks of remaining students = Sum of marks of all 15 students - Sum of marks of the first 8 students - Sum of marks of the last 8 students
- Sum of marks of remaining students = S - 376 - 440
- Sum of marks of remaining students = S - 816
8. We know that the average mark of all 15 students is 50. So, using the formula: Average = Sum/Number of values, we can write:
- S/15 = 50
- S = 750
9. Substituting the value of S in equation 8, we get:
- Sum of marks of remaining students = 750 - 816
- Sum of marks of remaining students = -66
10. Since we know the sum of marks of the remaining students, we can find the average mark of the remaining students using the formula: Average = Sum/Number of values.
- Average mark of the remaining students = (-66)/(15 - 8)
- Average mark of the remaining students = (-66)/7
- Average mark of the remaining students = -9.43 (approx)
11. Now, since we have the average mark of the remaining students, we can find the marks of the 8th student by multiplying the average mark of the remaining students by 7 and subtracting it from the sum of marks of the first 8 students.
- Marks of the 8th student = (Average mark of the first 8 students) * 8 - (Average mark of the remaining students) * 7
- Marks of the 8th student = 47 * 8 - (-9.43) * 7
- Marks of the 8th student = 376 + 66 (approx)
- Marks of the 8th student = 442 (approx)
Conclusion:
The marks of the 8th student will be approximately 442. Therefore, the correct answer is option B)
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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)56b)66c)70d)86Correct answer is option 'B'. Can you explain this answer?
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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)56b)66c)70d)86Correct answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 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)56b)66c)70d)86Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)56b)66c)70d)86Correct 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)56b)66c)70d)86Correct answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 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)56b)66c)70d)86Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)56b)66c)70d)86Correct answer is option 'B'. Can you explain this answer?.
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