How to find maximum value in a column with awk

Could you please try following, written and tested based on your shown samples in GNU awk.

awk '
!NF{
  if(max!=""){ print arr[max],max }
           max=""
  }
{
    max=( (max<$2) || (max=="") ? $2 : max )
    arr[$2]=$1
}
END{
  if(max!=""){ print arr[max],max }
}
'  Input_file

Explanation: Adding detailed explanation for above.

awk '                            ##Starting awk program from here.
!NF{                             ##if NF is NULL then do following.
  if(max!=""){ print arr[max],max }  ##Checking if max is SET then print arr[max] and max.
  max=""                         ##Nullifying max here.
  }
{
  max=( (max<$2) || (max=="") ? $2 : max )      ##Checking condition if max is greater than 2nd field then keep it as max or change max value as 2nd field.
  arr[$2]=$1                     ##Creating arr with 2nd field index and 1st field as value.
}
END{                             ##Starting END block of this program from here.
  if(max!=""){ print arr[max],max }  ##Checking if max is SET then print arr[max] and max.
}
' Input_file                     ##mentioning Input_file name here.