Last year the price per share of Stock N increased by p percent and the earnings per share of Stock N increased by q percent, where p is greater than q. By what percent did the ratio of price per share to earnings per share increase, in terms of p and q? Answers
A) (p-q)/(100+q) %	B) (100+q) %	C) 100*(p-q)/(100+q) %	D) 100*(p-q) %	E) p/q%
Let P = the old price per share; E = the old earning per share. Thus P/E is the price to earning ratio before the increases   After the increase the new price is: P*(1+p/100) and the new earning is: E*(1 +q/100)   The new P/E is: (1+p/100)P/(1+q/100)E   The Percent of P/E increase = (new P/E - P/E)/(P/E). Subsititute new P/E to the equation we have:   [(1+p/100)/(1+q/100)*P/E - P/E]/(P/E)*100%. Simplifly the expression and you should get the answer to be:   100*(p-q)/(100+q) %   Answer : 100*(p-q)/(100+q) %
<result>C</result>
Last year the price per share of Stock N increased by p percent and the earnings per share of Stock N increased by q percent, where p is greater than q. By what percent did the ratio of price per share to earnings per share increase, in terms of p and q?