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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

v=weight of empty vessel
p=weight of paint in full vessel
v+p=10v=total weight of full vessel
p=9v
let x=fraction of p remaining after total weight of full vessel is halved
v+9vx=5v
x=4/9
D
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Quick solved in 30 sec:

let's say the full vessel weights 100 kg, split as follows:
empty vessel 10 kg - paint 90 kg

Half of the weight of the full vessel is 50kg, split as follows:
empty vessel 10kg - paint 40kg

The ratio of the paint weights is 40/90, therefore answer is 4/9

Answer is D
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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

We can let the weight of the vessel when it’s filled with paint = 100, so the vessel itself weighs 10 and the paint weighs 90. If a partially filled vessel is one-half the weight of a completely filled vessel, then the partially filled vessel weighs 50. Since the vessel itself still weighs 10, the paint weighs 40. Since a completely filled vessel can be filled with paint that weighs 90, a partially filled vessel with paint that weighs 40 is 40/90 = 4/9 of a completely filled vessel with paint.

Answer: D
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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.

Assume that total weight of vessel filled with paint is 100 kg

Weight of the empty vessel = 10 % of 100 = 10 kg and the weight of the paint = 100 -10 = 90 kg

The weight of a partially filled vessel is one half that of a completely filled vessel

i.e weight of a partially filled vessel = 50 kg

So the weight of the paint in the vessel = 50 -10 = 40 kg.

Fraction of vessel that is filled = 40/90 =4/9

Option D is the answer.

Thanks,
Clifin j Francis
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