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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 24 Apr 2012, 16:49
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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%
(0) 55%
(E) 65%

Please some discussion about this convoluted problem ........
[Reveal] Spoiler: OA

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Re: Fringe-benefit costs represented what percent of employment? [#permalink] New post 24 Apr 2012, 19:20
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carcass wrote:
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%

Please some discussion about this convoluted problem ........


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.
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Re: Fringe-benefit costs represented what percent of employment? [#permalink] New post 25 Apr 2012, 02:49
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Bunuel wrote:
carcass wrote:
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%

Please some discussion about this convoluted problem ........


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.


As weighted average we have a distance between 3 and 5.5 (data points) = 3.5 (the average)

3 -----3.5------------------5.5

5.5 - 3.5 = 2.5 --------> the weight is more on 3 (3.5 is closer to 3 than 5.5) so 3.5 - 3 = 0.5

0.5/2.5= 0.2 ------> 20% Answer is B

In that quickly way is also correct Bunuel ??

thanks
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Re: A survey of employers found that during 1993 employment cost [#permalink] New post 18 Apr 2014, 23:04
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I preferred to do this by means of aligations


3-------------------------5.5

------------3.5-------------

2-------------------------0.5

Then,

0.5/2 = 1/4

1 part of X and 4 parts of Y

hence , 1/5 * 100 = 20%
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Re: A survey of employers found that during 1993 employment cost [#permalink] New post 08 Mar 2013, 22:52
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My Solution based on mixture rules:

S------------------------------FB
3-------------------------- 5.5

----------3.5-------------

5.5 -3.5 = 2 & 3.5 - 3 = 0.5

S: FB = 2: 1/2 = 4:1.

FB = 1/5 = 20%
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Re: Fringe-benefit costs represented what percent of employment? [#permalink] New post 24 Apr 2012, 19:18
carcass wrote:
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%
(0) 55%
(E) 65%

Please some discussion about this convoluted problem ........


Thsi question is bascially asking you to figure out that how much salary costs and fringe-benefit costs individually contribute to 3.5%.

salary costs - 3%
fringe-benefit costs - 5.5%
and both together contributed 3.5%..then salary costs contributed 20% Answer is (B)
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Re: A survey of employers found that during 1993 employment cost [#permalink] New post 27 Feb 2013, 05:27
According to the weighted average salary (s) and Fringe Benefits (F) contriution would come in the ratio: 0.5:2 or 1:4
so F=4/5 New costs. I am lost after this... The question asks the F= ?% Costs at the beginning
New cost (N) = 103.5 % Old cost (C). This is approximately 80%. How did we get 20%? What am I missing here
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Re: A survey of employers found that during 1993 employment cost [#permalink] New post 09 Mar 2013, 00:17
x+y=z
103x+105.5y=103.5z

now multiply the 1st equation with 103 -
103x+103y=103z
103x+105.5y=103.5z

2.5y=0.5z
y/z=5/25=1/5

ans is 20%
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Re: A survey of employers found that during 1993 employment cost [#permalink] New post 25 Apr 2015, 17:19
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Re: A survey of employers found that during 1993 employment cost [#permalink] New post 23 May 2015, 08:40
carcass wrote:
Bunuel wrote:
carcass wrote:
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%

Please some discussion about this convoluted problem ........


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.


As weighted average we have a distance between 3 and 5.5 (data points) = 3.5 (the average)

3 -----3.5------------------5.5

5.5 - 3.5 = 2.5 --------> the weight is more on 3 (3.5 is closer to 3 than 5.5) so 3.5 - 3 = 0.5

0.5/2.5= 0.2 ------> 20% Answer is B

In that quickly way is also correct Bunuel ??

thanks


I used the same method, taken from VeritasPrepKarishma post here: http://www.veritasprep.com/blog/2011/04 ... -mixtures/
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Re: A survey of employers found that during 1993 employment cost [#permalink] New post 27 May 2015, 12:36
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%
(0) 55%
(E) 65%
S = salary, F = fringe-benefit, E = employment cost
F/(S+F) x 100 = ?

S + .035S = 1.03S // F + .055F = 1.055F // S + F = E // E + .035E = 1.035E
1.03S + 1.055F = 1.035E = 1.035 (S + F)
1.03S + 1.055F = 1.035S + 1.035F
1.055F - 1.035F = 1.035S - 1.03S
.02F=.005S
(.02/.005)F=S
4F=S

F/(S+F) x 100 = ?
F/(4F + F) x 100 = (F/5F) x 100 = (1/5) x 100 since the variable cancels. The answer is 20.
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A survey of employers found that during 1993 employment cost [#permalink] New post 28 May 2015, 05:15
Expert's post
This is not a difficult question per se. And yet, because it has many information points, the question may seem confusing/convoluted.

A student who felt such a confusion in this question should represent the given information visually. For example, like this:

Image

From this image, it becomes clear that:

E = S + F . . . (1)
Ef (E final) = 1.03S + 1.055F . . . (2)

But we are given: Ef = 1.035E . . . (3)

Substituting (1) and (2) in (3), we get:

1.03S + 1.055F = 1.035(S+F)

From here on, the question is easy to solve.

The crux of this post is that if you find yourself getting overwhelmed by the given information, representing it visually helps. :)

Best Regards

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A survey of employers found that during 1993 employment cost   [#permalink] 28 May 2015, 05:15
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