An empty wooden vessel weighs 14% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.  Choose the correct option:
A) 6 / 13  B) 5 / 9  C) 1 / 24  D) 4 / 9  E) 2 / 5

Rationale: "an empty wooden vessel weighs 14 % of its total weight when filled with paint : vessel = 0.14 ( vessel + paint ) ; 14 v = v + p ( so the weight of completely filled vessel is 14 v ) p = 13 v ( so the weight of the paint when the vessels is completely filled is 13 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 14 v ; p ' = 6 v ( so the weight of the paint when the vessels is partially filled is 6 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p ' / p = 6 v / 13 v = 6 / 13 . answer : a ."
Answer: A