If in the army there is one officer for every 16 privates, how many officers are there in a regiment consisting of 1,105 officers and privates?

There are 16 privates for every
officer.

Therefore if there are x officers in the regiment,
then the number of privates is 16x. So the total number of officers and privates
together it is x+16x = 17x.

But the actual number
of officers and privates in the regiment is 1105. So both 17x and 1105 must be
same.

So 17x = 1105.

We divide
both sides by 17:

Therefore, x= 1105/17 =
65.

x is the number of officers we
assumed.

So the number of officers in the regiment is
65.