If in the army there is one officer for every 16 privates...?

Question

...how many officers are there in a regiment consisting of 1,105 officers and privates?

(A) 62

(B) 65

(C) 67

(D) 69

Answer 1

If there is one officer for every 16 privates, then in any given group of soldiers, 1/17 of them will be officers.  If we have a regiment of 1,105 officers and privates,

1105/17 = 65 will be officers.  Answer --> (B)

Answer 2

If there are k officers and exactly 16 privates for every officer, then the total number of soldiers is

16k + k = 1105

17k =1105

divide both sides by 17

k = 65

Answer 3

1105/17=

65

ans. there are 65 officers,(B)

Answer 4

Let o=number of officers and p=number of privates.

2 variables----->need 2 independent equations to solve for them.

Eq 1: o+p =1105

Eq 2: 16o=1p (There are 16 privates to 1 officer, so you will need 16 times the number of officers to equal the amount of privates)

Substitue Eq 2 into Eq 1

16o + o=17o=1105



o=65 (b)