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)

$\frac{100(k-m)}{100+m}$ %

$\Rightarrow$ Let the original price = 100 and original earning = 100

$\Rightarrow$ Original ratio of price to earning = $\frac{100}{100}=1$

$\Rightarrow$ New ratio,

$\Rightarrow$ Price increased by $k\%=100+\frac{k}{100}\times 100=100+k$

$\Rightarrow$ Earning increased by $m\%=100+\frac{m}{100}\times 100=100+m$

$\Rightarrow$ New ratio $=\frac{100+k}{100+m}$

$\Rightarrow$ Difference between the ratios are,

$\Rightarrow$ $\frac{100+k}{100+m}-1$

$\Rightarrow$ $\frac{(100+k)-(100+m)}{(100+m)}$

$\Rightarrow$ $\frac{(k-m)}{(100+m)}.$

$\Rightarrow$ Percent change in the ratios = $\frac{Differencebetweentheratios}{Originalratio\times 100}$

$\Rightarrow$ $\frac{\frac{(k-m)}{(100+m)}}{1\times 100}$

$\Rightarrow$ $\frac{100(k-m)}{(100+m)}\%$