Sum of degrees in tree $= L + I \times (n+1) - 1 = 10n + 50 ($Each leaf node has degree 1 and all internal nodes have degree $k+1,$ except root which has degree $k)$
So, number of edges $= 5n + 25 ($Number of edges in a graph (hence applicable for tree also) is half the sum of degrees as each edge contribute $2$ to the sum of degrees)
In a tree with $n$ nodes we have $n-1$ edges, so with $41+10 = 51$ nodes, there must be $50$ edges.
So, $5n + 25 = 50$
$\implies 5n = 25$
$\implies n = 5$