no...
there isn't enough information to assume "this and only this"
We don't know how much money the man had to start with
We only know the information from 4 transactions...
The first transaction he bought a goat and that goat cost $60
The second transaction he sold a goat, and that goat sold for $70
The sum of the first pair of transactions is $10
The third transaction a man bought a goat for $70
He then sold that goat for $80
The sum of that transaction is $10
The sum of both transactions, $10 + $10 = $20
There isn't another answer. The assumption you quoted about "loaning money and paying back" is made up information to justify an incorrect point.
If I buy a car one day and sell it for $10 more than I purchased it on the next day I made $10. If I go and buy another car and sell it for $10 more than I purchased it the next day, I made another $10. The transactions are independent of each other.
Now,
If the question says "a man uses
his last $60 to buy a goat and sell it for $70 and then
borrows $10 to buy a goat that costs $80 in order to sell that goat for $90,
how much does the man have after he pays back his debtor" then you and this other person would be right.
But as the question is written, four total transactions that leave the seller +$20 is pretty easily decipherable