GATE CSE 2014 | Set 2 | GA | Question: 9

Question

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 $2009$?

Comments

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

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@mehul vaidya it does not make any difference. when you get the data of year 2008 on 1st jan. 2009 you should not be concerned about exactly when the data was taken on 31st dec. 2008 or 1st jan. 2009.

Answer 1

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

Comments

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 ? 

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$Year$  $2008$ :- 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=$(\frac{New  value-Old value}{old value})*100$

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

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@Registered user 31 

they are asking this: "by what percent did the number of male students increase in 2009?"

if they were asking this: "what will be the increased number of male students in percentage in year 2009"

then this would have been ambiguous enough to be considered what you are saying because in this case it is unclear whether they are asking about the increased number itself or the total number after the increase.

Answer 2

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%

Comments

Upvoted. Yours is a good, generalised answer.

Maybe change the font to make it more readable, though.

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updated fonts.

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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 ” !

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@nocturnal123 what you are suggesting is correct. they should either solve like your answer using “$\dfrac{xM}{2F}  = 3$” or they (this answer + best answer) can just simply rename it like: "$\dfrac{M^{\prime}}{2F} = 3$"

So increase in $M = M^{\prime} - M = 6F- 2.5F = 3.5F$

Answer 3

https://gateoverflow.in/?qa=blob&qa_blobid=8558332009058325329

Answer 4

Simple concept

let boys =5, girls=2

now ratio is 2.5

in 2009 girls is doubled so girls=4

now boys=5+x/4=3

   x=7

calculate increase percent= (12-5)/5*100

                                        =140.