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

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26 Aug 2009, 03:30

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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?

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.

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.

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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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!

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.

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