In a school 10% students get 70 marks,25% students get 80 marks,15% students…
2025
In a school 10% students get 70 marks,25% students get 80 marks,15% students get 85 marks,25% students get 90 marks, remaining get 95 marks.What is the minimum number of students in the class if the avg. Of sum of marks is an even no.
Answer: A. 20 — Approach: Let the total number of students be n. The counts by marks are: 10% → n/10 students getting 70; 25% → n/4 students getting 80; 15% → 3n/20 students…
- A.
20
- B.
80
- C.
100
- D.
200
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Show answer & explanation
Correct answer: A
Approach:
Let the total number of students be n. The counts by marks are: 10% → n/10 students getting 70; 25% → n/4 students getting 80; 15% → 3n/20 students getting 85; 25% → n/4 students getting 90; remaining 25% → n/4 students getting 95.
For all these counts to be integers, n must be a multiple of the least common multiple of the denominators 10, 4, and 20, which is 20. So the smallest possible n is 20.
Compute the weighted average: 0.10·70 + 0.25·80 + 0.15·85 + 0.25·90 + 0.25·95 = 86, which is an even integer.
Conclusion: The minimum number of students in the class is 20.