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A survey of employers found that during 1993 employment cost

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A survey of employers found that during 1993 employment cost [#permalink] New post 25 Oct 2011, 09:30
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A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ?

(A) 16.5%
(B) 20%
(C) 35%
(D) 55%
(E) 65%

[Reveal] Spoiler:
I saw this question before. I followed the karishma method(veritas prep instructor). but i am getting wrong answer

w1/w2=a2-Aavg/Aavg-a1. Aavg=3.5(e.c),a1=3.0(s.c)/a2=5.5(f.c)
5.5-3.5/3.5-3.0.

please explain


OPEN DISCUSSION OF THIS QUESTION IS HERE: a-survey-of-employers-found-that-during-1993-employment-cost-168678.html
[Reveal] Spoiler: OA
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Re: A survey of employers found that during 1993 employment cost [#permalink] New post 25 Oct 2011, 16:11
TomB wrote:
154. A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefits costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993?
a. 16.5%
b. 20%
c. 35%
d. 55%
e. 65%

I saw this question before. I followed the karishma method(veritas prep instructor). but i am getting wrong answer

w1/w2=a2-Aavg/Aavg-a1. Aavg=3.5(e.c),a1=3.0(s.c)/a2=5.5(f.c)
5.5-3.5/3.5-3.0.

please explain

Can you link the method that you used?

This is how I did it:

Givens:
Fringe benefits = 5.5%
Salary = 3%
Total = 3.5%

Let X be the percentage fringe benefits represents out of total employment costs
Let Y be the percentage that salary represents out of total employment costs
The question asks you what X is

X*5.5% + Y*3% = 3.5% | should be obvious
X + Y = 100% | should be obvious
Y = 100% - X | equation to substitute out Y since we're solving for X

X*5.5% + (100% - X)3% = 3.5% | substitute out Y
5.5%X + 3% - 3%X = 3.5% | multiply the parenthesis
2.5%X = 0.5% | subtract 3% from both sides and add the X
X = 20% | multiply both sides by 40

Hence B
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Re: A survey of employers found that during 1993 employment cost [#permalink] New post 25 Oct 2011, 17:54
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Please look up 'alligation rule' that is usually linked with mixtures. Simple weighted average problems such as this one can be fixed in a few seconds.
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Re: A survey of employers found that during 1993 employment cost [#permalink] New post 25 Oct 2011, 18:09
DexDee wrote:
Please look up 'alligation rule' that is usually linked with mixtures. Simple weighted average problems such as this one can be fixed in a few seconds.

Kudos :-D

(5.5-3.5):(3.5-3) = y:x
2:0.5 = y:x

y:x must be 80%:20%
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Re: A survey of employers found that during 1993 employment cost [#permalink] New post 26 Oct 2011, 06:21
Hi

I find the method from the following link. Take a look at "karishma" post. there is link in that post about weighted averages
revenue-73058.html.

thanks
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Re: A survey of employers found that during 1993 employment cost [#permalink] New post 26 Oct 2011, 07:07
Hi i understand up to 2:0.5 (alligation rule). how did you get 80%:20%. please relate this to the question i.e "fringe benefit costs represented what percent of employment costs at the beginning or 1993". please explain
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Re: A survey of employers found that during 1993 employment cost [#permalink] New post 26 Oct 2011, 07:47
TomB wrote:
Hi i understand up to 2:0.5 (alligation rule). how did you get 80%:20%. please relate this to the question i.e "fringe benefit costs represented what percent of employment costs at the beginning or 1993". please explain


2 Parts for salary and 0.5 for fringe benefit. So making a total of 2+0.5=2.5.
So, Fringe benefit is 0.5/2.5*100=20%.

Hope this helps...
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Re: A survey of employers found that during 1993 employment cost [#permalink] New post 10 Oct 2014, 19:18
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Re: A survey of employers found that during 1993 employment cost [#permalink] New post 11 Oct 2014, 03:29
Expert's post
A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ?

(A) 16.5%
(B) 20%
(C) 35%
(D) 55%
(E) 65%

The amount by which employment costs rose is equal to 0.035(salary costs + fringe benefit costs);

On the other hand the amount by which employment costs rose is equal to 0.03*salary costs + 0.055*fringe benefit costs;

So, 35(S+F) = 30S+55F --> S = 4F --> F/S = 1/4 --> F/(S+F) = 1/(1+4) = 1/5 = 0.2.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-survey-of-employers-found-that-during-1993-employment-cost-168678.html
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Re: A survey of employers found that during 1993 employment cost   [#permalink] 11 Oct 2014, 03:29
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