[問題]天山 09-18

[mark-alan]

Q18:
Last year the price per share of Stock X increased by k percent and the earnings per shareof Stock X increased by m percent, where k is greater than m. By what percent did theratio 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) %

不會算..

[汪汪北鼻]

(1+k%)-(1+m%)/(1+m%)= 100(k-m)/100+m %:smile

[mark-alan]

看不懂......為什麼分母的式子是兩個上揚的比率相減........

[汪汪北鼻]

設p=1
e=1
比較好算

增加後
p=(1+k%)
e=(1+m%)
By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?

增加後-增加前=增加率
(1+K%)/(1+m%)-1/1=通分=(1+k%)-(1+m%)/(1+m%)= 100(k-m)/100+m %

[greenfox]

增加率應該是=(增加後-增加前)/增加前,這題沒影響是因為增加前的比率剛好等於1

[Kennethy]

為什麼可以設 price=1 跟earnings=1?

不是兩個是不同的東西嗎?

可以請大大再說明仔細一點嗎?


thanks

[antimissle]

e=original earnings
p=original price

#hint: by what percent ......increase

(1+k%)P/(1+m%)e - p/e

通分相減, 結果提出p/e即得該解!

[chris8888]

這樣說好了
By what percent did <== 多少%
the ratio of <== 這個比率
price per share to earnings per share <== 每股價格 to 每股獲利
increase <== 增加
===> 每股價格 to 每股獲利的比率, 增加了多少%
===> 我們先算出原先的每股價格對上每股獲利, 在算出後來的每股價格對上每股獲利
===> (後來的每股價格對上每股獲利 - 原先的每股價格對上每股獲利) / 原先的每股價格對上每股獲利 * 100% = 答案

演算 :
原先的每股價格對上每股獲利, 假設price per share => p, earnings => e ; p : e
後來的每股價格對上每股獲利, p(1+k/100) : e(1+m/100)
(p(1+k/100) / e(1+m/100) - p/e) / p/e => p(k-m)/100/e(1+m/100) / p/e
=> k-m/100 * 1/(1+m/100)
=> k - m / 100 + m * 100% <== 補上%
=> (100(k - m) / (100 + m))%