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Manager  Joined: 19 Aug 2009
Posts: 77
The weight of an iron bucket increases by 33.33% when filled  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 28% (02:18) correct 72% (02:25) wrong based on 53 sessions

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The weight of an iron bucket increases by 33.33% when filled with water to 50% of its capacity. Which of these may be 50% of the weight of the bucket when it is filled with water( assume the weight of bucket and its capacity in kg to be integers?

1. 7 kg
2. 6 kg
3. 5 kg
4. 8 kg
Senior Manager  Joined: 23 Jun 2009
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Re: Percentage again  [#permalink]

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1
W=weight of bucket
V=volume of bucket
W + 0,5V = 1,33W
so 0,5V = 0,33W
it wants us (W+V)/2 that is (W + 0,66W)/2= 0,83W But we do not know anything else. So anyone can be. But the sentence in paranthesis gives us a clue. Capacity of bucket and weight of bucket are integer. So W and 0,66W is integer. i.e. W and 2/3W is integer. So we can assume that W is a multiple of 3 (say 3n) . And 0,66 W is a multiple of 2 (say 2n). So they make a multiple of 5 together (3n+2n).
So the answer, IMO, 3.
Director  Joined: 23 Apr 2010
Posts: 509
Re: Percentage again  [#permalink]

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1
Bunuel, can you please look at this question? I agree with the solution by maliyeci but I don't think that multiple of 2 + multiple of 3 equals multiple of 5 (eg., 18+4 = 22). Thank you.
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Re: Percentage again  [#permalink]

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virtualanimosity wrote:
Q.
The weight of an iron bucket increases by 33.33% when filled with water to 50% of its capacity. Which of these may be 50% of the weight of the bucket when it is filled with water( assume the weight of bucket and its capacity in kg to be integers?

1. 7 kg
2. 6 kg
3. 5 kg
4. 8 kg

rets try some numbers.
Say IronB = 6 kg EMPTY so filled with 50% water you have a 1/3*6 = 2 kg water weight. so adding the rest of the bucket with water will naturally increase it by another 2kg so you have 2+2+6 = 10 thus 50% of 10 = 5.
Hope it helps
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Re: Percentage again  [#permalink]

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shaselai wrote:
virtualanimosity wrote:
Q.
The weight of an iron bucket increases by 33.33% when filled with water to 50% of its capacity. Which of these may be 50% of the weight of the bucket when it is filled with water( assume the weight of bucket and its capacity in kg to be integers?

1. 7 kg
2. 6 kg
3. 5 kg
4. 8 kg

rets try some numbers.
Say IronB = 6 kg EMPTY so filled with 50% water you have a 1/3*6 = 2 kg water weight. so adding the rest of the bucket with water will naturally increase it by another 2kg so you have 2+2+6 = 10 thus 50% of 10 = 5.
Hope it helps

Hey thanks a lot. My algebra is not that strong, your explanation a lot more sense to me!

Thanks,
Dawgie
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Math Expert V
Joined: 02 Sep 2009
Posts: 58353
Re: Percentage again  [#permalink]

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virtualanimosity wrote:
Q.
The weight of an iron bucket increases by 33.33% when filled with water to 50% of its capacity. Which of these may be 50% of the weight of the bucket when it is filled with water( assume the weight of bucket and its capacity in kg to be integers?

1. 7 kg
2. 6 kg
3. 5 kg
4. 8 kg

$$\frac{bucket}{50% \ water}=\frac{3}{1}$$ --> $$\frac{bucket}{100% \ water}=\frac{3}{1+1}=\frac{3}{2}$$ --> as the weight of bucket and its capacity in kg are integers then the weight of bucket full with water will be a multiple of 3+2=5 (5, 10, 15, 20, ...) --> half of this weight will be 2.5, 5, 7.5, 10, ... Only answer matching this possible values is 5 kg.

Answer: 3 (5 kg).
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Re: Percentage again  [#permalink]

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Guys, thanks for your explanations but I don't get either.

In shaselai's solution I don't understand if we can pick a different number than 6.

In Bunuel's solution I don't get how he got the first expression.

Thank you.
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Joined: 02 Sep 2009
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Re: Percentage again  [#permalink]

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nonameee wrote:
Guys, thanks for your explanations but I don't get either.

In shaselai's solution I don't understand if we can pick a different number than 6.

In Bunuel's solution I don't get how he got the first expression.

Thank you.

Given that weight of 50% of water is 1/3 (33.33%) of the weight of bucket --> so if bucket=3, then 50% water=1.
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Re: Percentage again  [#permalink]

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Bunuel, thanks a lot. I got it.
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Re: The weight of an iron bucket increases by 33.33% when filled  [#permalink]

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Let,the weight of the bucket = x;
So, weight of the bucket when it contains 50% water = (x+x/3)=4x/3 [since, the weight increases by 33.33%]

So when it contains 100% water the weight will be = (4x/3)+(x/3)=5x/3
[As, the weight of 50% water is x/3 other 50% will also be x/3]

Now , the total weight = 5x/3
So , half will be 5x/6
Now according to the qs weight of bucket and its capacity must be integer
so,if we check the options,
5x/6 = 7 (wrong)
5x/6 = 6 (wrong)
5x/6 = 5 (correct,since in that case x will be an integer)
5x/6 = 8 (wrong) so,option 3 is correct

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Re: The weight of an iron bucket increases by 33.33% when filled  [#permalink]

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Bunuel wrote:
virtualanimosity wrote:
Q.
The weight of an iron bucket increases by 33.33% when filled with water to 50% of its capacity. Which of these may be 50% of the weight of the bucket when it is filled with water( assume the weight of bucket and its capacity in kg to be integers?

1. 7 kg
2. 6 kg
3. 5 kg
4. 8 kg

$$\frac{bucket}{50% \ water}=\frac{3}{1}$$ --> $$\frac{bucket}{100% \ water}=\frac{3}{1+1}=\frac{3}{2}$$ --> as the weight of bucket and its capacity in kg are integers then the weight of bucket full with water will be a multiple of 3+2=5 (5, 10, 15, 20, ...) --> half of this weight will be 2.5, 5, 7.5, 10, ... Only answer matching this possible values is 5 kg.

Answer: 3 (5 kg).

hi

The weight of a bucket increases by 33.33% that is 1/3 when filled with 50% of water, so when filled with 100% of water the wight will increase by 2/3....so far so good ...however, can you please speak few more words about the operation "3+2 = 5"...?

Is this something as such that the ratio of water to bucket is 2:3...so, the water and weight in kg have to be divisible by (2+3), for the condition to hold true that weight and water in kg are integers....?

please say to me whether this is okay .....?

thanks in advance , man ...
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Re: The weight of an iron bucket increases by 33.33% when filled  [#permalink]

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_________________ Re: The weight of an iron bucket increases by 33.33% when filled   [#permalink] 25 Mar 2019, 19:24
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