Gaurav, Raj and Krishna went to a fair, where they entered a lucky draw contest and were given tokens, which are all four digit numbers. Just before the contest, Krishna and Raj lost their tokens, while Gaurav’s token was torn into two pieces, each piece containing two digits of the four. His token number was 2025, the smallest number amongst the 3 tokens. The first piece of Gaurav’s token had 20 written on it and the second had 25 written on it.
They did not remember the numbers in the other two tokens exactly, but Krishna claimed he knew a common feature of all three tokens. When the numbers on the two pieces of Gaurav’s token were added and this sum was squared, the original token number was obtained (first piece first). The same applied to all three tokens. Hearing this Raj said, “Also, my token number is bigger than the sum of your token numbers.” Gaurav claimed that there are exactly three 4-digit numbers satisfying this criterion and told them their token numbers. What were the token numbers of Raj and Krishna; and how did Gaurav compute these?