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Difficulty:
55%
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Question Stats:
62% (02:04) correct
38%
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wrong
based on 271
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An empty wooden vessel weighs 10% 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.
A. 3/5
B. 5/9
C. 1/24
D. 4/9
E. 2/5
A. 3/5
B. 5/9
C. 1/24
D. 4/9
E. 2/5
05 Jun 2014, 03:15
Kudos
Bookmarks
Empty.................. Paint............... Total
Say total weight when completely filled with paint = 100
10....................... 90 .................. 100
Say x quantity paint is removed
10 .......................... 90-x............. 100-x
Equation would come up as
\(\frac{1}{2} * 100 = 100-x\)
x = 50
90 - x = 90 - 50 = 40
Fraction \(= \frac{40}{90} = \frac{4}{9}\)
Answer = D
Say total weight when completely filled with paint = 100
10....................... 90 .................. 100
Say x quantity paint is removed
10 .......................... 90-x............. 100-x
Equation would come up as
\(\frac{1}{2} * 100 = 100-x\)
x = 50
90 - x = 90 - 50 = 40
Fraction \(= \frac{40}{90} = \frac{4}{9}\)
Answer = D
05 Jun 2014, 02:45
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Bookmarks
balan88
An empty wooden vessel weighs 10% 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.
A. 3/5
B. 5/9
C 1/24
D. 4/9
E. 2/5
A. 3/5
B. 5/9
C 1/24
D. 4/9
E. 2/5
An empty wooden vessel weighs 10% of its total weight when filled with paint:
Vessel = 0.1(Vessel + Paint);
10V = V + P (so the weight of completely filled vessel is 10V)
P = 9V (so the weight of the paint when the vessels is completely filled is 9V).
The weight of a partially filled vessel is one half that of a completely filled vessel:
V + P' = 1/2*10V;
P' = 4V (so the weight of the paint when the vessels is partially filled is 4V).
What fraction of the vessel is filled?
So, we need to find the ratio of the weight of the paint when the vessel is completely filled to the weight of the paint when the vessel is partially filled:
P'/P = 4V/9V = 4/9.
Answer: D.
