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

Question

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%

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

quantumliner · Answer

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%

Answer is B. 25%

grichagupta · Answer

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

IdiomSavant · Answer

Payroll  
Weight 1: 105

Infrastructure  
Weight 2: 101

Average: 102

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

Payroll is 25% of operating expense.

ScottTargetTestPrep · Answer

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%

Answer: B

amanguptaiitr · Answer

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%

riyadhrazzaq · Answer

# Backsolving
Let, total = 100
After 2% increase, total is = 102

## Option D, 40%
P = 40, I = 60
+5% on P is 40.8
+1% on I is 63.6
new total after the increment is 104.4, which is >102

## Option B, 25%
P = 25, I = 75
+5% on P is 26.25
+1% on I is 75.75
new total after the increment is 102, which is = 102

Therefore, correct ans is *B*

naikabhishekjanu · Answer

Operating expense initially- OE= PE + IS (eqn 1)

Operating expense later on OE(102/100)=PE(105/100)+ IS(101/100) - eqn 2

Multiply equation 1 by 101 and the subtract it from equation 2

Thus final equation will be OE= 4PE or PE is 25 % of OE

luisdicampo · Answer

Deconstructing the Question

Operating expenses consist of payroll expenses and infrastructure spending.

Payroll increased by   5\%   and infrastructure increased by  1\% .

The overall operating expenses increased by  2\% .

We want to find what percent of the operating expenses payroll represented initially.

Step-by-step

Let the initial fraction of payroll be

x

Then infrastructure represents

1-x

The overall percent increase is the weighted average of the two increases.

5x+1(1-x)=2

Simplify

5x+1-x=2

4x+1=2

4x=1

x=0.25

Thus payroll represented

25\%

of the operating expenses at the beginning of the year.

Answer B

pappal · Answer

given o=p+i or i=o-p
now from the given condition,
1.05p + 1.01(o-p)=1.02o
0.04p=0.01o
p/o=1/4=25% 
so B

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

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