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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]

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24 Apr 2012, 17:49
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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]

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24 Apr 2012, 20:20
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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]

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25 Apr 2012, 03:49
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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]

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19 Apr 2014, 00:04
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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]

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08 Mar 2013, 23:52
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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]

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24 Apr 2012, 20:18
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]

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27 Feb 2013, 06:27
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]

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09 Mar 2013, 01:17
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]

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25 Apr 2015, 18:19
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Re: A survey of employers found that during 1993 employment cost [#permalink]

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23 May 2015, 09:40
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]

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27 May 2015, 13:36
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]

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28 May 2015, 06:15
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:

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

Japinder
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A survey of employers found that during 1993 employment cost   [#permalink] 28 May 2015, 06:15
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# A survey of employers found that during 1993 employment cost

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