Answer:
Narcisse could have given 17
Explanation:
Given that Narcisse and Aristide have numbers of arcade tokens in the ratio 7 : 3
Let Narcisse have 7x and Aristide 3x respectively
If d tokens are given from Narcisse to Aristide, new belongings
7x-d, 3x+d
Ratio is 6:5

i.e. So x should be a multiple of 11
least number of x =11
Verify:
Narcisse and Aristide have intially 77 and 33.
Narcisse gave 17 to Aristide
New are 60 and 50 making ratio 6:5
So answer is 17