The other tutor's answer is incorrect.

There are 5 ways to choose each digit as 1,3,5,7,or 9,
so the total number of 4 digit numbers with only odd
digits is 5^4 or 625.  Think of all 625 numbers added 
up like this: 

 1111
 1113
 1135
 ....
 ....
 9995
 9997
+9999
-----

Each of the 4 columns of 625 digits contains the
same number of 1's as 3's as 5's as 7's and as 9's.  
Therefore each of the 4 columns of 625 digits 
contains 125 1's, 125 3's, 125 5's, 125 7's, and 125 9's

So the sum of each column of digits is 

125(1 + 3 + 5 + 7 + 9) = 125(25) = 3125
 
The column of thousands digits accounts for 3125000 toward the sum
The column of  hundreds digits accounts for  312500 toward the sum
The column of      tens digits accounts for   31250 toward the sum
The column of      ones digits accounts for    3125 toward the sum
------------------------------------------------------------------
So the sum is is the sum of those numbers-> 3471875               
   
An easier way to do it is to realize it is the same as if all
the digits were the average of the odd digits, which is 5. So
the answer is the same as if every number among the 625 were 
replaced by 5555.  So 5555×625 = 3471875.

Edwin