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Percentage [#permalink] New post 25 Mar 2009, 23:06
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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) %
6
C. [100(k – m)] / (100 + k) %
D. [100(k – m)] / (100 + m) %
E. [100(k – m)] / (100 + k + m) %
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Re: Percentage [#permalink] New post 19 Dec 2010, 16:49
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gettinit wrote:
I still don't understand how you got from the percent increase equation to the final selection of D? What steps were taken to arrive at the simplified D expression?


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) %

Original price - x
Original earnings - y
Original ratio price per earnings - \frac{x}{y}

Increased price - x(1+\frac{k}{100})=\frac{x(100+k)}{100}
Increased earnings - y(1+\frac{m}{100})=\frac{y(100+m)}{100}
New ratio price per earnings - \frac{x(100+k)}{y(100+m)}

General formula for percent increase or decrease, (percent change):

Percent=\frac{Change}{Original}*100

\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=(\frac{100+k}{100+m}-1)100=\frac{100(k-m)}{100+m}

Answer: D.
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Re: Percentage [#permalink] New post 26 Mar 2009, 13:45
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milind1979 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) %
6
C. [100(k – m)] / (100 + k) %
D. [100(k – m)] / (100 + m) %
E. [100(k – m)] / (100 + k + m) %


Price Per Share (PPS) = x
Earning Per Share(EPS) = y

Increased PPS = x(1+k/100)
Increased EPS = y(1+m/100)

% increase in the ratios (PPS/EPS) = {[x(100+k)]/[y(100+m)] - (x/y)} / (x/y)

On Simplifying, % increase = [100(k-m)] / (100 + m) % , hence (D).
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Re: Percentage [#permalink] New post 19 Dec 2010, 16:39
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I still don't understand how you got from the percent increase equation to the final selection of D? What steps were taken to arrive at the simplified D expression?
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Re: Percentage [#permalink] New post 23 Dec 2010, 18:52
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Ahh thanks Bunuel that clears things up. It was the multiplication with a 100 I was leaving off.
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Re: Percentage [#permalink] New post 23 Dec 2010, 19:26
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It should be D. Tricky one.
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Re: Percentage [#permalink] New post 23 Dec 2010, 22:57
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@ bunuel

I am good at calculating % and hardly face any difficulty with % probs or any other time,rate, distance probs

But, whenever i see the probs asked in terms of alphabetical notions instead of actual nos, i take a lot of time and make lot many mistakes. what is the best approach in addressing such probs e.g. if this same problem had real nos instead of k,m etc, i could easily solve it , but this alpha notations made me take some 3 to 4 mins for this prob
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Re: Percentage   [#permalink] 23 Dec 2010, 22:57
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