The average marks of a student in 8 subjects is 87. Of these, the highest…
2024
The average marks of a student in 8 subjects is 87. Of these, the highest marks are 2 more than the one next in value. If these two subjects are eliminated, the average marks of the remaining subjects are 85. What are the highest marks now obtained by him?
- A.
94
- B.
91
- C.
89
- D.
96
Show answer & explanation
Correct answer: A
Concept: When a group is split into two subsets, the total marks removed equals the group's original total minus the remaining subset's total. If two unknown values have a known sum and a known difference, each value can be found by solving the two equations together.
Total marks for all 8 subjects = 8 x 87 = 696.
Total marks for the remaining 6 subjects = 6 x 85 = 510.
Marks removed (sum of the two eliminated subjects) = 696 - 510 = 186.
Let the highest mark be x; since it is 2 more than the next-highest, the next-highest is x - 2.
x + (x - 2) = 186, so 2x - 2 = 186, so 2x = 188, so x = 94.
Cross-check: with x = 94, the next-highest is 92, and 94 + 92 = 186, matching the total removed; adding this pair back to the remaining total gives 186 + 510 = 696 = 8 x 87, confirming the original average of 87.