To answer this type of question while practicing, always prefer derivation method instead of hit and trial
let total number of nodes =N
so N= total number of leaves nodes(say L) +total number no internal nodes (n )
edge (E)= N-1 => E= n + L -1 ............(1)
again edge (E)= (n* k) + (L*0) ............(2) //{because only internal nodes are involved in forming an edge}
so from equation 1 and 2
n + L -1 = n*k
L=nk - n + 1
L=n(k-1)+ 1