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) %

Answer

这题问的是价格（price）和收入（earning）的比率增加了多少

设最初的价格为P，收入E，那么原始价格与收入的比率是P/E

增加后的价格和收入分别是P(1+K%),E(1+M%)

那么两者增加后的比率是[P(1+K%)]/[E(1+M%)]

比率的增量是[P(1+K%)]/[E(1+M%)]-P/E＝[P(k%-m%)]/[E(1+m%)] (通分那些计算过程我就省略拉～)，最后去掉P/E就是比率的增量了

怎么可以直接去掉P/E呢? 而且后面化简出来是: (K%-M%)/(100+M)% , 这个和[100(k-m)]/(100+m) % 是相等的吗?

你误会题目和答案的表示了…

题目是问” By what percent did the ratio of price per share to earnings per share increase,” 问的是”percent”，所以当然要把[P(k%-m%)]/[E(1+m%)] 先除上P/E，再乘以100%，来得到变化的百分比﹙这是第一个关键，妳先想一下﹚

另外一个问题就是 结果应该是(k%-m%)/(1+m%) >> (k%-m%)/(100+m)% >> (k-m)/(100+m) >> 然后乘上100% >> 100(k-m)/(100+m) % 这个部分的关键在于”百分比%”是针对整个数﹙100(k-m)/(100+m)﹚，而不是只有分母﹙(100+m)﹚ 妳参考看看…