Lot of correct answers to the puzzle – the ones who sent the correct answer include Siddharth Mulherkar (good to see you on the blog!), Sandeep Singhal, Ritesh Banglani, Aditya, Pratik Poddar, Suman Saraf, Karan Sharma (my nephew who gave me the puzzle), Prakhar Prakash, Amit Mittal and Shruti Mittal. Well done all!

I am taking the liberty of reproducing the answer directly from Ritesh Banglani. The answer is 6666600.

If you fix a number for one decimal position, the other numbers can be arranged in 4! ways.
The sum of all those numbers is 4! * (1+3+5+7+9)
If we do this for every decimal place, we have to add (10^4+10^3+10^2+10^1+10^0)
So the total sum is 4! * (1+3+5+7+9) * (10^4+10^3+10^2+10^1+10^0) = 6666600

Hope you all enjoyed the puzzle!