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# An empty metal box weigh 10% of its total weights when field

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VP
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An empty metal box weigh 10% of its total weights when field [#permalink]

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03 Jan 2005, 23:46
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An empty metal box weigh 10% of its total weights when field with water. if the weight of partly filled box is 1/2 that of a completely filled box, what fraction of the box is filled?

a. 3/5
b. 5/9
c. 1/2
d. 4/9
e. 2/5
Senior Manager
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04 Jan 2005, 04:08
I'll go with (D)

Not the most elegant way, but an approach, nevertheless, on the basis of POE.

Let the weight of the partially filled box be 100 => weight of water = 90 and weight of box = 10. If the completely filled box weighs double the partially filled box, it follows that just less than half the box is filled with water (because the weight of the completely filled box would include the weight of the box as well). This rules out (a), (b), (c) and (e) and leaves us with (d).

It would be great if you could post the OA with explaination.
Director
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04 Jan 2005, 05:26
My take on this is :

since the empty metal box weigh 10% of its total weight if wt of box is 100 the box + water = 1.1*100 = 110 when completely filled

new weight is 1/2 of completely filled = 110/2 = 55

fraction filled is 55 /110 = 1/2

My answers is 1/2
Director
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04 Jan 2005, 08:12
Get D

Let wt of box + water = x
Wt of box = 0.1x
So, wt of water = 0.9x

Let the wt of water in the when partly filled = y
We get
0.1x +y = 0.5x, so y = 0.4x

0.9x corresponds to wt of water when box is completely filled. So, (0.9x --> 1)
0.4x wt of water corresponds to what fraction of box ? (0.4x --> ?)

It would be 0.4x/0.9x = 4/9
VP
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04 Jan 2005, 08:26
"D" for me. Let 100 be wt of box when full then:

wt of box = 10
wt of water = 90

Let wt of water when partially ful be x then

100/ 2 = 10 + x ===> x = 40

90 water makes it full so 40 makes it 40/90 = 4/9.
VP
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04 Jan 2005, 20:06
maaverick wrote:
I'll go with (D)

Not the most elegant way, but an approach, nevertheless, on the basis of POE.

Let the weight of the partially filled box be 100 => weight of water = 90 and weight of box = 10. If the completely filled box weighs double the partially filled box, it follows that just less than half the box is filled with water (because the weight of the completely filled box would include the weight of the box as well). This rules out (a), (b), (c) and (e) and leaves us with (d).

It would be great if you could post the OA with explaination.

Thanx all. good explanaions, maaverick, gyatri and banerjee.
04 Jan 2005, 20:06
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# An empty metal box weigh 10% of its total weights when field

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