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 this**Quote:**

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

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?
_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"