vaivish1723 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. \(\frac{k}{m} %\)
B. \((k – m) %\)
C. \(\frac{100(k – m)}{(100 + k)} %\)
D. \(\frac{100(k – m)}{(100 + m)} %\)
E. \(\frac{100(k – m)}{(100 + k + m)} %\)
dave13 wrote:
Bunuel wrote:
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):
\(Percent=\frac{Change}{Original}*100\)
\(\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=\frac{100(k-m)}{100+m}\)
Answer: D.
hello
generis, so what book did you read today ?
please tell me in two words
the more i tag you the more new english words i learn from you that will help me during RC
and of course working on math
can you please help me to understand this
\(\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=\frac{100(k-m)}{100+m}\)
why do we deduct price from percentage or is it increased price denoted as percentage ?
And why are we dividing by fraction \(\frac{x}{y}\), ??
we already have fraction \(\frac{x}{y}\) in numerator ...
have a lovely jovely day / night
Hi
dave13 ,
Are you on a mission lately to find demonic
algebra?
I am teasing you. I'm always happy to help if I can.
You wrote:
can you please help me to understand thisQuote:
\(\frac{\frac{x(100+k)}{y(100+m)}-\frac{x}{y}}{\frac{x}{y}}100=\frac{100(k-m)}{100+m}\)
why do we deduct price from percentage . . .If you refer to \(\frac{x}{y}\):
1) \(\frac{x}{y} = \frac{P}{E}\) ratio
\(x\) = original price per share
\(y\) = original earnings per share
2)
Bunuel is not deducting price from percentage
\(\frac{x}{y}\) is the ORIGINAL or OLD \(\frac{P}{E}\)
ratioHe is deducting old \(\frac{P}{E}\) ratio from new \(\frac{P}{E}\) ratio
which must be done
in order to calculate percent changeSee below
or is it increased price denoted as percentage ?
Not sure what "it" refers to.
I think it is \(\frac{x}{y}\)
The
numerator, \(x\), is indeed
The new price expressed in terms of percent increase (good catch):
\(x\) = original price per share
That price increases by
\(k\) percent
\(k\) percent = \(\frac{k}{100}\)So
\(x\) increases by
\(k\) percent
OF \(x\):
\(x + (\frac{k}{100}*x)\) = new price
Simplify. Factor out the
\(x\)New Price =
\(x(1 + \frac{k}{100})\)Simplify inside the parentheses.
\((1 +\frac{k}{100})\)\(1 = \frac{100}{100}\), so
\(\frac{100}{100} + \frac{k}{100} = \frac{100 +k}{100}\)The \(x\) outside the parentheses is still there. Result:
\(\frac{x(100+k)}{100}\)I can't decide whether you're confused about
subtracting
\(\frac{x}{y}\) or
\(m\) from
\(k\)Either way, both subtractions happen because . . .
This expression is needed to calculate percent change.Percent change can be defined as
\(\frac{Change}{Original} * 100\)
To make the concept of "change" clearer,
percent change can be defined equivalently as
\(\frac{New - Old}{Old} * 100\)
New: \(\frac{x(100+k)}{y(100+m)}\)
Old: \(\frac{x}{y}\)
Try plugging those values into the
second variation of the percent change formula.
And why are we dividing by fraction \(\frac{x}{y}\)? we already have fraction \(\frac{x}{y}\) in numerator ... We are dividing by \(\frac{x}{y}\) because we are
calculating percent change.
\(\frac{x}{y}\) is . . . the old / original
\(\frac{P}{E}\) ratio
See the footnote, which contains an example of fraction to fraction percent change.
This problem is hard.
It contains a strange sort of ratio
(price-per-share to earnings-to-share is
hugely influential but not, IMO, intuitive);
the difference of ratios
(new and old, in which price growth k percent > earnings growth m percent);
AND a percent increase.
You are not a fan
of substituting values, it appears.
If you have not already, please
try going through both of
Bunuel's posts
with pencil and paper in hand.
By "both posts" I mean the one you quoted and the one
HERE.
I hope that helps.
Example of percent change with a fraction
(please note that I must divide by the original \(\frac{1}{4}\)):
Last year at the zoo, 1 animal in 4 was a newborn
This year at the zoo, 2 animals in 5 were newborns
By what percent did the ratio of newborns to all animals increase?
Percent change:
\((\frac{New - Old}{Old} * 100)\)
\(\frac{\frac{2}{5}-\frac{1}{4}}{\frac{1}{4}}*100\)
\(\frac{\frac{3}{20}}{\frac{1}{4}}*100 = \frac{3}{20}*\frac{4}{1}*100=\)
\(\frac{12}{20}*100=.6 * 100 = 60\) percent increase
P.S. The book I [am] read[ing] today? In two words?
How will you know about this astonishing book? Its title consists of more than two words.
What kind of restriction is THAT? _________________
Welcome back, America.
—Anne Hidalgo, Mayor of Paris