Problem Solving

Q: A Eunuch was throwing a boomerang repeatedly . Each time it threw it, the boomerang rebound back and hit the eunuck itself such that the eunuck depleted its energy each time it was struck back and could throw the boomerang only half the distance of the previous throw. If the eunuch throw the boomerang for the first time for the distance of 16 mts , find the total distance the boomerang has travelled when the eunuck threw it for the 10th time( i.e before getting hit back the 11th time)?

(A)63(15/16) [mixed fraction]

(B)37(5/16) [mixed fraction]

(C)67(11/16) [mixed fraction]

(D)49(13/16) [mixed fraction]

(E)31(11/16) [mixed fraction]

Are we to assume the distance is the full distance travelled there and back, or just the range of each throw? As it is not explicit in the question, I will use the former.

Individual distances:
1st throw = 16 * 0.5^0
2nd throw = 16 * 0.5^1
3rd throw = 16 * 0.5^2
nth throw = 16 * 0.5^(n-1)
10th throw = 16 * 0.5^(9)

Total distance = 16 * (1 + 0.5 + 0.5^2 + 0.5^3 +... ...+ 0.5^9) < 32

So answer (E)31(11/16) [mixed fraction]

If the question gives distance as range of each throw, then double the answer to
get answer (A)63(15/16) [mixed fraction]