Q18:

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) %

Suppose the price is x per share and the earning is y per share. The question asks the change of the ratio x/y.

On the price side, the increased price is (1+k%)x

On the earning side, the increased earning is (1+m%)y

Hence, the new ratio is ((1+k%)x)/((1+m%)y).

The percentage of change of the ratio is

100%*(((1+k%)x)/((1+m%)y)-x/y)/(x/y)

Choose D.

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