Average of 5 integers is 38 and all the numbers are between 0 and 50 (both inclusive). In these 5 numbers, a is the minimum. If exactly 3 of them are more than 32, find the difference between the minimum and the maximum value of a.

Question

In an examination, the average marks of 4 girls and 6 boys is 24 . Each of the girls has the same marks while each of the boys has the same marks. If the marks of any girl is at most double the marks of any boy, but not less than the marks of any boy, then the number of possible distinct integer values of the total marks of 2 girls and 6 boys is

Answer 1

The average marks for all students is \(38\).
The total marks are \(5\times38=190\).
The maximum scores of the remaining students are \(= 50 +49 +48 + 32 = 179\).
The minimum possible score is \(= 190 - 179 = 11\).
\(⇒\) The maximum possible score is \(=31\).
The difference between the minimum and the maximum value is \(31-11 = 20\).

Therefore, the answer is \(20\).

Average of 5 integers is 38 and all the numbers are between 0 and 50 (both inclusive). In these 5 numbers, a is the minimum. If exactly 3 of them are more than 32, find the difference between the minimum and the maximum value of a.

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