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# An empty wooden vessel weighs 10% of its total weight when

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Intern
Joined: 04 Jun 2014
Posts: 1
An empty wooden vessel weighs 10% of its total weight when [#permalink]

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Updated on: 05 Jun 2014, 03:14
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Difficulty:

55% (hard)

Question Stats:

63% (01:39) correct 37% (01:44) wrong based on 160 sessions

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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

Originally posted by balan88 on 05 Jun 2014, 02:23.
Last edited by balan88 on 05 Jun 2014, 03:14, edited 3 times in total.
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Joined: 02 Sep 2009
Posts: 47101
Re: An empty wooden vessel weighs 10% of its total weight when [#permalink]

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05 Jun 2014, 02:45
2
balan88 wrote:
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

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.

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Re: An empty wooden vessel weighs 10% of its total weight when [#permalink]

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05 Jun 2014, 03:15
4
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 $$= \frac{40}{90} = \frac{4}{9}$$

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An empty wooden vessel weighs 10% of its total weight when [#permalink]

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Updated on: 12 Aug 2017, 12:06
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

Originally posted by gracie on 04 Nov 2015, 18:44.
Last edited by gracie on 12 Aug 2017, 12:06, edited 1 time in total.
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Re: An empty wooden vessel weighs 10% of its total weight when [#permalink]

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04 Dec 2017, 02:32
1
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

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Re: An empty wooden vessel weighs 10% of its total weight when   [#permalink] 04 Dec 2017, 02:32
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