Stock EPS problem

[anantbhatia]

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) %
6
C. [100(k - m)] / (100 + k) %
D. [100(k - m)] / (100 + m) %
E. [100(k - m)] / (100 + k + m) %

OA D

[Rahul@gurome]

Let price per share of Stock X = x and earnings per share of Stock X = y
Increased price of Stock X = x + k% of x = x(1 + k/100) = x(100 + k)/100
Increased earnings per share of Stock X = y + m% of y = y(1 + m/100) = y(100 + m)/100
New ratio of price per share to earnings per share = x(100 + k)/100 / y(100 + m)/100 = x(100 + k)/y(100 + m)

Increase in ratio of price per share to earnings per share = [{(100 + k)/(100 + m) * (x/y) / (x/y)} - 1]*100
= [100(k - m)] / (100 + m) %

The correct answer is [spoiler](D)[/spoiler].