In a class of 150 students, 40% of the students got 45 marks on average and 46…
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In a class of 150 students, 40% of the students got 45 marks on average and 46 % of the students got 60 marks on average. The average marks for the total class are 55. Find the average marks secured by the rest of the students.
Answer: B. 67.14 — Solution: Find the average marks of the remaining students. Given: Total number of students = 150 Overall average marks = 55 Also: 46% of students have…
- A.
45.5
- B.
67.14
- C.
56.89
- D.
62.33
Attempted by 24 students.
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Correct answer: B
Solution: Find the average marks of the remaining students.
Given:
Total number of students = 150
Overall average marks = 55
Also: 46% of students have average 60, and 40% of students have average 45.
Concept used:
Total marks = Average × Number of students
Calculations:
Total marks for the class = 150 × 55 = 8250.
Number of students in 46% group = 0.46 × 150 = 69; their marks = 69 × 60 = 4140.
Number of students in 40% group = 0.40 × 150 = 60; their marks = 60 × 45 = 2700.
Marks contributed by these two groups = 4140 + 2700 = 6840.
Remaining marks = 8250 − 6840 = 1410.
Remaining students = 150 − (69 + 60) = 21.
Average for remaining students = 1410 ÷ 21 = 67.142857... ≈ 67.14 (rounded to two decimal places).
Answer: The average marks secured by the remaining students is 67.14.