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The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students doubled in $2009$, by what percent did the number of male students increase in $2009$?

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this question is ambiguous , it does not mention whether reading taken on 1 Jan or 31 Dec of particular  year.

In 2008 $\dfrac{M}{F}$ ratio is $2.5$

Assume $250$ Males, $100$ Females.

In 2009 $\dfrac{M}{F}$ ratio is $3.$ Also total no of females doubled

Females $=100\times 2 = 200.$

So, $\dfrac{M}{F} = 3 \implies \dfrac{M}{200}= 3$

$\implies M = 200\times 3 = 600.$

Increase in Male Students  $= 600 - 250 = 350$

Increase $=\left(\dfrac{350}{250}\right)\times 100 \%= 140 \%$

why you assumed Male as 250 and female 100. shall we assume both male and female as 100 ?
Then male: female ratio will not be 2.5. So, this is a wrong choice.

Why are we doing the step "Increase in Male Students  = 600 - 250 = 350" consider a case where 100 increased to 300, it should be called a 300% increase, right ? Similarly if 250 increased to 600, should it not be called (600/250)*100 % increase ?

$Year$  $2008$ :- Let Male$=$$M_{1} and Female=$$F_{1}$

Given $\frac{M_{1}}{F_{1}}=2.5$  -------->>>Equation 1

$Year$  $2009$ :- Let Male$=$$M_{2} and Female=$$F_{2}$

Given $\frac{M_{2}}{F_{2}}=3$ ---------->>>Equation 2

Given $F_{2}=2*F_{1}$   ---------->>>Equation 3

From Equation 1 : $M_{1}=2.5F_{1}$

From Equation 2 and 3 : $M_{2}=3F_{2}=6F_{1}$

So % increase in number of males=$(\frac{New value-Old value}{old value})*100$

$=(\frac{6F_{1}-2.5F_{1}}{2.5F_{1}})*100=140$%

In 2008, Let M males and F females be there, so

M/F = 2.5 , so M= 2.5F

In 2009, as females doubled

M/2F = 3, so M = 6F

So increase in M is (6F- 2.5F) = 3.5F

So percentage increase, (3.5F/2.5F ) * 100 = 140%

Upvoted. Yours is a good, generalised answer.

Maybe change the font to make it more readable, though.
updated fonts.
In “M/2F = 3”, you included 2F, since it is mentioned in question that number of female students is getting doubled. Why are you not including the fact, that M has also change by some “x”, factor.

I think, there should be “xM/ 2F  = 3 ” !