An empty wooden vessel weighs 20% 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.	Options
A) 3 / 5 B) 5 / 9 C) 1 / 24 D) 9 / 19 E) 2 / 5

Rationale: an empty wooden vessel weighs 20 % of its total weight when filled with paint : vessel = 0.2 ( vessel + paint ) ; 20 v = v + p ( so the weight of completely filled vessel is 10 v ) p = 19 v ( so the weight of the paint when the vessels is completely filled is 19 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 20 v ; p ' = 9 v ( so the weight of the paint when the vessels is partially filled is 9 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 = 9 v / 19 v = 9 / 19 . answer : d .
Answer: D