求解GWD24-4-17

li43119

答案是D，不会算。
Last year the price per share of Stock Xincreased by k percent and the earnings per share of Stock Xincreased by m percent, where k is greater than m.  By what percent did the ratio of price pershare 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) %

yongsf

是选择D吧
过程是这样的设去年的ratio of price pershare to earnings per share是P/E,由于P增长了k%,所以今年的P是P(1+K%);由于k增长了m%，所以今年的E是E(1+m%)。所以今年的ratio of price pershare to earnings per share是P(1+K%/E(1+m%)。
要求的是ratio of price pershare to earnings per share的增长的比例：
[P(1+K%)/E(1+m%) - P/E] / P/E
化简一下，上下同时约去 P/E，得到　(k% - m%)/(1 + m%)
再次化简得到　(k - m)/(100 + m)
这就是D

li43119

多谢！