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In one alloy there is 12% chromium while in another alloy...

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In one alloy there is 12% chromium while in another alloy... [#permalink] New post 21 Feb 2013, 06:54
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In one alloy there is 12% chromium while in another alloy it is 8%. 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.

A. 8.8%
B. 9%
C. 9.2%
D. 8.6%
E. 8.4%
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Re: In one alloy there is 12% chromium while in another alloy... [#permalink] New post 21 Feb 2013, 06:58
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(15x.12 + 35x.08)/(15+35) x100=9.2
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Re: In one alloy there is 12% chromium while in another alloy... [#permalink] New post 21 Feb 2013, 07:01
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antoxavier wrote:
In one alloy there is 12% chromium while in another alloy it is 8%. 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.

A. 8.8%
B. 9%
C. 9.2%
D. 8.6%
E. 8.4%


The amount of chromium in the new 15+35=50 kg alloy is 0.12*15+0.08*35=4.6 kg, so the percentage is 4.6/50*100=9.2%.

Answer: C.
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Re: In one alloy there is 12% chromium while in another alloy... [#permalink] New post 23 Mar 2015, 20:01
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Re: In one alloy there is 12% chromium while in another alloy... [#permalink] New post 23 Mar 2015, 20:23
Expert's post
Hi All,

This question is essentially a 'Weighted Average" question, so you can solve it in a few different ways. There is a built-in 'shortcut' in these types of questions that is worth noting (since it can save you some time). As long as the RATIO of the items is the same as what is described in the prompt, the amount of each item doesn't matter.

Here, we're told that we have 15kg of the first alloy and 35kg of the second. That is a ratio of 15:35, which reduces to 3:7. As long as THAT ratio is maintained, we will get the exact same answer as we would if we use 15kg and 35kg.

So, if we had 3 kg of the first alloy and 7kg of the second, the math would be a little easier. We'd have....

[3(.12) + 7(.08)]/(3+7) =
(.36 + .56)/(10) =
.92/10 =
9.2%

Final Answer:
[Reveal] Spoiler:
C


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Re: In one alloy there is 12% chromium while in another alloy... [#permalink] New post 25 Mar 2015, 00:18
Answer = C = 9.2%

\(\frac{\frac{12}{100} * 15 + \frac{8}{100} * 35}{35+15} * 100 = 9.2%\)
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Re: In one alloy there is 12% chromium while in another alloy... [#permalink] New post 25 Mar 2015, 09:12
"In one alloy there is 12% chromium while in another alloy it is 8%. 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy."

The two part are melted in a ratio of 3 to 7.
Hence : (3*12% + 7*8%)/10 = 9.2%
Re: In one alloy there is 12% chromium while in another alloy...   [#permalink] 25 Mar 2015, 09:12
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