For 16 privates we have 1 officer

for 16x2 privates we have 2 officers

for 16x3 privates we have 3 officers

in general for 16 x n privates n officers and total strength of officers and privates = 16 n + n = 17 n which in this case is given to be 1105 thus n = 1105/17 = 65

hence we have 65 officers