[求助]一道GWD数学题

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) %

Set P as share price, E as earning per share, x as percent of increase of "price per share to earnings per share", which can also be recognized as shares. Therefore,

P*(1+k%)/E(1+m%) = P*(1+x%)/E   =>  x= 100(k-m)/(100+m)

Here, x represents the percent, not including "%". If it asks for the "percentage", you should add "%" after the formula

上面的答案转自http://bbs..org/dispbbs.asp?BoardID=20&replyID=464639&id=163091&skin=0

设原来的Price为P，增长后的Price为P(1+k%)，再设原来的earnings为E，增长后的earnings为E(1+m%),所以increase的ratio= {[P(1+k%)/E(1+m%)]-P/E}/(P/E)=[(1+k%)/(1+m%)]-1=(k%-m%)/(1+m%)=(k+m)/(100+m).

由于答案要用percent表示所以要化为[100(k-m)]/(100+m) %，选D。