Question

Five students,including Amit,appear for an examination in which possible marks are integers between 0 and 50,both inclusive.The average marks for all the students is 38 and exactly three students got more than 32.If no two students got the same marks and Amit got the least marks among the five students,then the difference between the highest and lowest possible marks of Amit is

• A. 21
• B. 24
• C. 20
• D. 22

Answer 1

The Correct Option is C

Let's break down the problem step by step:
1. The average marks for all five students is 38,and the sum of their marks is \(190(5\times38)\).
2. Exactly three students got more than 32.This means that two students got less than or equal to 32.
3. Amit got the least marks among the five students.This implies that Amit's score should be minimized to maximize the scores of the other two students.
4. To find the minimum marks scored by Amit,we need to maximize the score of the remaining two students.The maximum scores they can get are 50 and 49,as any higher marks would violate the given condition that no two students got the same marks.
5. The maximum possible sum of the remaining two students' scores is 50+49=99.
6. Now,subtract the maximum possible sum of the remaining students scores (99) from the total sum of marks (190) to find the minimum possible score of Amit:190-99=91.
So, the difference between the highest and lowest possible marks of Amit is: 31(highest)-11(lowest) = 20.

Answer 2

Given that, the average marks for all the students is 38.
Then,
Total marks \(= 5 \times 38 = 190\)
To find the minimum marks scored by Amit, we need to maximise the score of remaining students.
Maximum scores sum of remaining students,
\(= 50 + 49 + 48 + 32\)
\(= 179\)
Minimum possible score of Amit,
\(= 190 - 179\)
\(=11\)
Given, Amit scored least i.e. maximum possible score of Amit is \(31\).
Then, the difference between the highest and lowest possible marks of Amit,
\(= 31 -11\)
\(= 20\)

So, the correct option is (C): \(20\)