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# Last year the price per share of Stock X increased by k

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Last year the price per share of Stock X increased by k [#permalink]

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11 Feb 2007, 05:05
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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) %
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Re: PS - Percents increase (Tough) [#permalink]

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11 Feb 2007, 08:15
TOUGH GUY wrote:
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) %

Assuming

Last year
Price per share = P/S = 1
Earning per share = E/S = 1
Ratio of Price Per Share to Earning per share = (P/S)/(E/S) = 1/1 = 1

This year
Price per share = (P/S)' = 1 + k/100 = (100 + k)/100
Earning per share = (E/S)' = 1 + m/100 = (100 + m)/100
Ratio of Price Per Share to Earning per share = (100 + k)/(100 + m)

Ratio of price per share to earnings per share increase in what percent

= [(P/S)' - (P/S)] / (P/S)

=( [(100 + k)/(100 + m)] - 1)/1 = (k-m)/(100 + m)

Change to percent (x100) = 100(k-m)/(100 + m)
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Re: PS - Percents increase (Tough) [#permalink]

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11 Feb 2007, 08:22
TOUGH GUY wrote:
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) %

Suppose last year's price was p and the earnings per share was e

This year, the price is p+pk/100 and the earnings were e+em/100

The ratio has increased from A=p/e to B=(p + pk/100)/(e+em/100)

B-A=p(k-m)/(e(100+m))

so 100%(B-A)/A= 100(k-m)/(100+m)%

D

Easier to pick numbers: if k=50 and m=25, ratio increases by 20%, which is given by choice D
Re: PS - Percents increase (Tough)   [#permalink] 11 Feb 2007, 08:22
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