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.
`(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 1

(D).
`\%\,change=(100(k-m))/((100+m))`

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,

`((100+k)x)/((100+m)y)`

Now,

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

`\%\,change=(((100+k)x)/((100+m)y)-(x)/(y))/((x)/(y))* 100\\\%\,change=((x)/(y)(((100+k)-(100+m))/((100+m))))/((x)/(y))* 100\\\%\,change=(100(k-m))/((100+m))`

Therefore, the correct option is (D).