rsarashi wrote:Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?
A. k/m %
B. (k - m) %
C. [100(k - m)] / (100 + k) %
D. [100(k - m)] / (100 + m) %
E. [100(k - m)] / (100 + k + m) %
OAD
An alternate approach is to combine plugging in values with a bit of algebra.
Old ratio:
Let the original price = 100 and the original earnings = 100.
Original ratio of price to earnings = 100/100 = 1.
New ratio:
Price increased by k% = 100 + (k/100)(100) = 100 + k.
Earnings increased by m% = 100 + (m/100)(100) = 100 + m.
New ratio = (100+k)/(100+m).
Difference between the ratios:
(100+k)/(100+m) - 1 = [(100+k) - (100+m)] / (100+m) = (k-m)/(100+m).
Percent change in the ratios = (difference between the ratios)/(original ratio) * 100:
[(k-m)/(100+m)] / 1 * 100 = [100(k-m)] / (100+m).
The correct answer is
D.
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