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
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Karishma
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