Question

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.

Answer 1

Given, the average marks for all the students is $38$.
Total marks $= 5\times38=190$
Maximum scores of remaining students $= 50 +49 +48 + 32 = 179$
Minimum possible score $= 190 - 179 = 11$
$⇒$ Maximum possible score $=31$
The difference between the minimum and the maximum value of a $= 31-11 = 20$

So, the answer is $20$.