Question

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. $\frac{k}{m}$B. (k–m)C. $\frac{100(k-m)}{(100+k)}$D. $\frac{100(k-m)}{(100+m)}$E. $\frac{100(k-m)}{(100+k+m)}$

Answer 1

Answer:

(D). $\%\,change=\frac{100(k-m)}{(100+m)}$

Step-by-step explanation:

In the question,

Let us say the Price per Share, initially = 100x

and,

Earnings per Share = 100y

So,

Percent increase in Price per share = k%

Percent increase in Earning per share = m%

So,

New Price per Share = 100x + kx = (100 + k)x

and,

New Earnings per Share = 100y + my = (100 + m)y

Now,

Initial ratio of Price per Share to Earnings per share = 100x/100y = x/y

And,

Final ratio of Price per Share to Earning per share is,

$\frac{(100+k)x}{(100+m)y}$

Now,

Percent increase in the ratio of Price per share to Earnings per share is,

$\%\,change=\frac{\frac{(100+k)x}{(100+m)y}-\frac{x}{y}}{\frac{x}{y}}\times 100\\\%\,change=\frac{\frac{x}{y}(\frac{(100+k)-(100+m)}{(100+m)})}{\frac{x}{y}}\times 100\\\%\,change=\frac{100(k-m)}{(100+m)}$

Therefore, the correct option is (D).