A firm's annual revenue grows twice as fast as its costs. In : Problem Solving (PS)

WoundedTiger

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A firm's annual revenue grows twice as fast as its costs. In [#permalink]

27 Mar 2013, 08:15

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A firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?

A. 700
B. 1000
C. 1300
D. 1600
E. 2000

I found this problem quite difficult to be solved under 2 mins. Will be really keen to know if there are any shortcuts to handle such Questions.
Would you rate this problem a 700 + ??

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SVaidyaraman

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Re: A firm's annual revenue grows twice as fast as its costs. In [#permalink]

16 Aug 2013, 19:23

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1. Let the revenues and costs in 2007 be r1 and c1 respectively. We have r1-c1=-1000
2. Let revenues in 2008 be r2 and c2 respectively. We have r2-c2=0
3. Let revenues and costs in 2009 be r3 and c3 respectively. we have r3=1.44r1.
4. Since the growth rate of sales is constant, growth rate per year is 20%. growth rate of costs is half of that which is 10%
5. (2) can be written as 1.2 r1-1.1 c1=0
6. Solving for (1) and (5), we have c1=12000 andr1=11000
7. r3=1.44*11000= 15840 and c3=1.21*12000=14520
8. Therefore profit in 2009=15840-14520=1320

The answer should be $1320
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Re: A firm's annual revenue grows twice as fast as its costs [#permalink]

27 Mar 2013, 12:48

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mridulparashar1 wrote:

A firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?

A. 700
B. 1000
C. 1300
D. 1600
E. 2000

First solve for how much revenue is increasing each year:
R2008 = R2007*(1+x)
R2009 = R2007*(1+x)^2=1.44*R2007
(1+x)^2 = 1.44
1+x=1.2
x=0.2 aka revenue increases 20% each year and cost increases 10% annually

Next solve for R2007 and C2007:
R2007 = C2007 - 1000
1.2*R2007 - 1.1*C2007 = 0
1.2*[C2007 - 1000] - 1.1*C2007 = 0
0.1*C2007 = 1,200
C2007 = 12,000
R2007 = 11,000

Finally find 2009 profits:
Profit2009 = 1.44*11,000 - 1.21*12,000
Profit2009 = 15,840 - 14,520
Profit2009 = 1320
Answer: C

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KarishmaB

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Location: Pune, India

Re: A firm's annual revenue grows twice as fast as its costs. In [#permalink]

17 Sep 2014, 22:24

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WoundedTiger wrote:

A firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?

A. 700
B. 1000
C. 1300
D. 1600
E. 2000

I found this problem quite difficult to be solved under 2 mins. Will be really keen to know if there are any shortcuts to handle such Questions.
Would you rate this problem a 700 + ??

Revenues increased by 44% in 2 years. Rate of revenue increase per year is the same. So

$(1 + x)^2 = 1.44$
$x = 20%$

So revenue increases by 20% per year and since cost increases at half the rate, cost increases by 10% every year.

Say 2007 revenue is R and 2007 cost is C.
We know C = R + 1000 ....(I)

In 2008, they break even.
So 1.1*C = 1.2R
Substituting from (I), 1.1*(R + 1000) = 1.2R
R = 11,000
C = 12,000

In 2009,
Profit = (1.2)^2*R - (1.1)^2C = 1.44*11,000 - 1.21*12000 = 1320

Asifpirlo

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Re: A firm's annual revenue grows twice as fast as its costs. In [#permalink]

16 Aug 2013, 17:36

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2013gmat wrote:

A firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?

A $700
B $1000
C $1300
D $1600
E $2000

can anyone explain above question ?
thanks

By strict definitions, revenue can not be negative. But in the corrupt world of finance, revenue is a number between positive infinity and negative infinity depending on how the upper management instruct the finance people how to lie on the spreadsheets in their submissions to the Securities and exchange commission.

jaituteja

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Re: A firm's annual revenue grows twice as fast as its costs. In [#permalink]

17 Aug 2013, 02:13

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SravnaTestPrep wrote:

1. Let the revenues and costs in 2007 be r1 and c1 respectively. We have r1-c1=-1000
2. Let revenues in 2008 be r2 and c2 respectively. We have r2-c2=0
3. Let revenues and costs in 2009 be r3 and c3 respectively. we have r3=1.44r1.
4. Since the growth rate of sales is constant, growth rate per year is 20%. growth rate of costs is half of that which is 10%
5. (2) can be written as 1.2 r1-1.1 c1=0
6. Solving for (1) and (5), we have c1=12000 andr1=11000
7. r3=1.44*11000= 15840 and c3=1.21*12000=14520
8. Therefore profit in 2009=15840-14520=1320

The answer should be $1320

How did you deduce that "growth rate per year is 20%."????

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SVaidyaraman

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Joined: 17 Dec 2012

Posts: 591

Location: India

Re: A firm's annual revenue grows twice as fast as its costs. In [#permalink]

17 Aug 2013, 03:32

Expert Reply

jaituteja wrote:

SravnaTestPrep wrote:

1. Let the revenues and costs in 2007 be r1 and c1 respectively. We have r1-c1=-1000
2. Let revenues in 2008 be r2 and c2 respectively. We have r2-c2=0
3. Let revenues and costs in 2009 be r3 and c3 respectively. we have r3=1.44r1.
4. Since the growth rate of sales is constant, growth rate per year is 20%. growth rate of costs is half of that which is 10%
5. (2) can be written as 1.2 r1-1.1 c1=0
6. Solving for (1) and (5), we have c1=12000 andr1=11000
7. r3=1.44*11000= 15840 and c3=1.21*12000=14520
8. Therefore profit in 2009=15840-14520=1320

The answer should be $1320

How did you deduce that "growth rate per year is 20%."????

The rate can be calculated from the formula (1+r/100) ^2 = 1.44 , which will give r=20
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aks456

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A firm's annual revenue grows twice as fast as its costs. [#permalink]

13 Feb 2014, 09:06

A firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?
a)$700
b)$1000
c)$1300
d)$1600
e)$2000
Also whats the level of this question ?

L

Bunuel

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Joined: 02 Sep 2009

Posts: 92760

Re: A firm's annual revenue grows twice as fast as its costs. [#permalink]

13 Feb 2014, 10:26

Expert Reply

akankshasoneja wrote:

A firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?
a)$700
b)$1000
c)$1300
d)$1600
e)$2000
Also whats the level of this question ?

Merging similar topics. Please refer to the solutions above.

As for the difficulty level, I'd say it's ~650-700.
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pretzel

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Re: A firm's annual revenue grows twice as fast as its costs. In [#permalink]

16 Apr 2014, 08:14

I am lost. Can't solve it.

m3equals333

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Re: A firm's annual revenue grows twice as fast as its costs. In [#permalink]

17 Apr 2014, 22:26

tough one for sure.

3rd year revenue going up by 44% = 1st year revenue * (12^2/10^2)

so 2nd year revenue is 1st year revenue * (12/10) --> 1st year revenue + 1st year revenue (2/10)

so growth rate of revenue is 20% and costs is 10%

ronr34

Senior Manager

Joined: 08 Apr 2012

Posts: 259

Re: A firm's annual revenue grows twice as fast as its costs. In [#permalink]

17 Sep 2014, 14:29

SravnaTestPrep wrote:

1. Let the revenues and costs in 2007 be r1 and c1 respectively. We have r1-c1=-1000
2. Let revenues in 2008 be r2 and c2 respectively. We have r2-c2=0
3. Let revenues and costs in 2009 be r3 and c3 respectively. we have r3=1.44r1.
4. Since the growth rate of sales is constant, growth rate per year is 20%. growth rate of costs is half of that which is 10%
5. (2) can be written as 1.2 r1-1.1 c1=0
6. Solving for (1) and (5), we have c1=12000 andr1=11000
7. r3=1.44*11000= 15840 and c3=1.21*12000=14520
8. Therefore profit in 2009=15840-14520=1320

The answer should be $1320

Something is messing up my calculations.
I substituted the amount by which C and R go up with X.
This meant that at 2009 we needed to find out : R*x^4 - C*X^2.
Since X^4 = 1.44 -> X^2 = 1.2
And that's why I multiplied C by 1.2 and not 1.21.
Why is this wrong?

L

KarishmaB

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Joined: 16 Oct 2010

Posts: 14815

Location: Pune, India

Re: A firm's annual revenue grows twice as fast as its costs. In [#permalink]

17 Sep 2014, 22:15

Expert Reply

ronr34 wrote:

SravnaTestPrep wrote:

1. Let the revenues and costs in 2007 be r1 and c1 respectively. We have r1-c1=-1000
2. Let revenues in 2008 be r2 and c2 respectively. We have r2-c2=0
3. Let revenues and costs in 2009 be r3 and c3 respectively. we have r3=1.44r1.
4. Since the growth rate of sales is constant, growth rate per year is 20%. growth rate of costs is half of that which is 10%
5. (2) can be written as 1.2 r1-1.1 c1=0
6. Solving for (1) and (5), we have c1=12000 andr1=11000
7. r3=1.44*11000= 15840 and c3=1.21*12000=14520
8. Therefore profit in 2009=15840-14520=1320

The answer should be $1320

Something is messing up my calculations.
I substituted the amount by which C and R go up with X.
This meant that at 2009 we needed to find out : R*x^4 - C*X^2.
Since X^4 = 1.44 -> X^2 = 1.2
And that's why I multiplied C by 1.2 and not 1.21.
Why is this wrong?

C and R do not go up by the same rate X. You are given that revenue grows twice as fast as cost. So if rate of revenue growth is X, rate of cost growth is X/2.

G

ShashankDave

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A firm's annual revenue grows twice as fast as its costs. In [#permalink]

11 Jul 2016, 10:30

WoundedTiger wrote:

A firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?

A. 700
B. 1000
C. 1300
D. 1600
E. 2000

I found this problem quite difficult to be solved under 2 mins. Will be really keen to know if there are any shortcuts to handle such Questions.
Would you rate this problem a 700 + ??

First of all..+1 for the question.
I got the right answer..but the only thing I felt eerie about this problem is that it has a lot of calculations to be done under the given timing constraints..Experts..please suggest something about the calculations this has. And what level would you classify this problem as..

zw504

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GMAT 1: 680 Q49 V33

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GMAT 3: 710 Q50 V36

GPA: 3.4

A firm's annual revenue grows twice as fast as its costs. In [#permalink]

24 Jul 2016, 20:41

Profit=Revenue-Cost

2007:
-1000=R1-C1

2008:
0=(1+2X%)R1-(1+X%)C1

2009:
P3=(1+2X%)^2*R1-(1+X%)^2*C1

we've already known that R3=1.44R1, so (1+2X%)^2=1.44, X=10

we put X=10 back to the equation of 2008:
0=1.2R1-1.1C1, and we have 1.2R1=1.1C1, which we could combine with the equation of 2007.
Then we have C1=12000, R1-11000

Finally, take C1 and R1 into the equation of 2009 and we got P3=15840-14520=1320

Thanks,

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