rahulvsd 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
Another approach is to
guess and check.
Revenues:
An increase of 44% over 2 years implies an increase of 20% each year.
To illustrate:
100 + .2(100) = 120.
120 + .2(120) = 144.
Percent increase = (144-100)/100 = 44%.
Costs:
Since the revenues grow twice as fast, the costs increase 10% each year.
Given that the loss in 2007 is $1000, the revenues in 2007 are almost certainly a multiple of 1,000.
Let's start with a nice, round number.
Case 1: Revenues in 1007 = 10,000.
Since the loss = 1000, the costs = 11,000.
2008:
Revenues = 10,000 + .2(10,000) = 12,000.
Costs = 11,000 + .1(11,000) = 12,200.
In order to break even, the revenues needs to increase just a bit.
Case 2: Revenues in 2007 = 11,000.
Since the loss = 1000, the costs = 12,000.
2008:
Revenues = 11,000 + .2(11,000) = 13,200.
Costs = 12,000 + .1(12,000) = 13,200. Success!
2009:
Revenues = 13,200 + .2(13,200) = 15,840.
Costs = 13,200 + .1(13,200) = 14,520.
Profit = 15,840 - 14,520 = 1320.
The closest answer is
C.
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