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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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+11 votes
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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

$\dfrac{M}{F} = 3$

$\dfrac{M}{200}= 3$

$M = 200\times 3 = 600.$

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

increase =$\left(\dfrac{350}{250}\right)\times 100 \%= 140 \%$
answered by Veteran (49.5k points)
edited
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 ?

hey aakash i also works at persi , pingala 2 nd floor

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

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

–2 votes
140 %
answered by (7 points)
–3 votes

May I know why every one considering range 2008 to 2009 for " If the number of female students doubled in 2009". Range could be 2009 to 2010. In that case solution would be

Ans :  m/f = 3 (for 2009)    -------------(1)

m1 / f1 = 2 (for 2010) where f1 =  2*f (as no of females doubled)

putting f1 in first equation

m1/2f = 2               ----------------(2)

and from  (1) and (2)

m1 =  4m/3

% increase (m1-m)/m =  33%

Guys please do comment and like , this is my first answer in GateOverflow

answered by (49 points)
–5 votes
The ratio is 3:1 given . So if females is x then there are 3x males. Now it number of girls doubles then number of boys has to double in order to keep the ratio as 3:1 . So girls is 2x and boys is 6x. The % increase in boys is (6x-3x)/(x+3x)*100 = 3/4*100 = 75%
answered by Boss (7.5k points)
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