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# At a certain company, operating expenses are measured as the sum of

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Math Expert
Joined: 02 Sep 2009
Posts: 59587
At a certain company, operating expenses are measured as the sum of  [#permalink]

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27 Mar 2017, 03:22
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Difficulty:

45% (medium)

Question Stats:

67% (02:01) correct 33% (02:28) wrong based on 75 sessions

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At a certain company, operating expenses are measured as the sum of payroll expenses and infrastructure spending. During the last fiscal year, payroll expenses increased by 5 percent and infrastructure spending increased by 1 percent. If overall operating expenses increased by 2 percent during the fiscal year, then payroll expenses represented what percent of operating expenses at the beginning of the fiscal year?

A. 20%
B. 25%
C. 33%
D. 40%
E. 50%

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Joined: 24 Apr 2016
Posts: 316
Re: At a certain company, operating expenses are measured as the sum of  [#permalink]

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27 Mar 2017, 10:32
Year Prior to Last Fiscal Year

Let Payroll expenses: 100P
Let Infrastructure expenses: 100I
Total Expenses: 100 (P+I)

Last Fiscal Year

Payroll expenses increased by 5%: 105P
Infrastructure expenses increased by 1%: 101I
Total Expenses: 105P+101I

overall operating expenses increased by 2 percent during the fiscal year. i.e.

1.02 * 100 (P+I) = 105P+101I

102P+102I = 105P+101I
I=3P

payroll expenses represented what percent of operating expenses at the beginning of the fiscal year = 100P *100/100(P+I)

= 100P/(P+3P) %

= 100P/4P = 100/4 = 25%

Intern
Joined: 13 Dec 2016
Posts: 41
Re: At a certain company, operating expenses are measured as the sum of  [#permalink]

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03 May 2017, 06:12
2
Let Payroll Expenses = x
Infrastructure Spending = y

Operating Expenses = x+ y

Last fiscal year,

1.02 (x+y) = 1.05x+ 1.01 y
simplyfying, 0.01 y = 0.03 x
or x/y = 1/3

Therefore, x/ (x+y) = 1/4 = 25%

hence, ans is B
Manager
Joined: 14 Sep 2016
Posts: 59
Concentration: Finance, Economics
Re: At a certain company, operating expenses are measured as the sum of  [#permalink]

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03 May 2017, 07:42
1
1
Bunuel wrote:
At a certain company, operating expenses are measured as the sum of payroll expenses and infrastructure spending. During the last fiscal year, payroll expenses increased by 5 percent and infrastructure spending increased by 1 percent. If overall operating expenses increased by 2 percent during the fiscal year, then payroll expenses represented what percent of operating expenses at the beginning of the fiscal year?

A. 20%
B. 25%
C. 33%
D. 40%
E. 50%

Payroll
Weight 1: 105

Infrastructure
Weight 2: 101

Average: 102

105-102 / 102-101 = 3:1 ratio

Payroll is 25% of operating expense.
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Re: At a certain company, operating expenses are measured as the sum of  [#permalink]

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06 May 2017, 17:30
1
Bunuel wrote:
At a certain company, operating expenses are measured as the sum of payroll expenses and infrastructure spending. During the last fiscal year, payroll expenses increased by 5 percent and infrastructure spending increased by 1 percent. If overall operating expenses increased by 2 percent during the fiscal year, then payroll expenses represented what percent of operating expenses at the beginning of the fiscal year?

A. 20%
B. 25%
C. 33%
D. 40%
E. 50%

We can let the payroll expenses at the beginning of the year = p and the infrastructure spending at the beginning of the year = f.

We are given that payroll expenses increased by 5% and infrastructure spending increased 1%, causing an overall increase of 2%. Thus:

1.05p + 1.01f = 1.02(p + f)

105p + 101f = 102p + 102f

3p = f

Since operating expenses are represented by p + f, we have:

p/(p + f) = p/(p + 3p) = p/4p = 1/4 = 25%

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Intern
Joined: 21 Jun 2016
Posts: 3
Re: At a certain company, operating expenses are measured as the sum of  [#permalink]

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20 Mar 2019, 09:48
Lets take:
i = infrastructure expense
p = payroll
o = operating

Here is the info we have:
a) o = i + p (last fiscal)
b) 2% o = 1% i + 5% p (current fiscal)

Divide everything by o - total operating expense. We get
a) 1 = i/o + p/o --> i/o = 1 - p/o
b) 2 = i/o + 5 p/o --> i/o = 2 - 5 p/o

Equate a) and b)
--> 1 - p/o = 2 - 5 p/o
--> 4 p/o = 1
--> p/o = 1/4 = 25%
Re: At a certain company, operating expenses are measured as the sum of   [#permalink] 20 Mar 2019, 09:48
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