the average of 30 integers is 5. among these 30 integers, there are exactly 20 which do not exceed 5. what is the highest possible value of the average of these 20 integers

We are given that the average of 30 integers is 5
So, the sum of these 30 integers will be (30*5=150)
Now, we are told that there are 20 integers which are less than 5 and hence 10 integers must be greater than 5
Now, to make the average of the first 20 integers which do not exceed 5 is maximum, their sum is maximum
Now, Sum of first 20 integers+ sum of remaining 10 integers greater than 5=150
Sum of remaining 10 integers greater than 5 will have to be minimised
Let us assume that all 10 numbers are (5+1) [the next possible integer above the overall average]
Hence, the sum of the remaining 10 integers is (6*10=60)
Hence, the sum of the initial 20 integers is =150-60=90
This gives us the average of =90/20=4.5
Hence, the required integers are: 4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5

the total of all 30 integers is 150 because their average is 5. The other 10 integers have to be more than 5, because only 20 integers exceed 5 so, we take those as 6 each. Their sum is 60, so the 20 integers have a sum of 150-60=90. Therefore, their average is 90/20=4.5