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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 $2009$?

edited | 1.5k views

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 =$\left(\dfrac{350}{250}\right)\times 100 \%= 140 \%$
edited
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why you assumed Male as 250 and female 100. shall we assume both male and female as 100 ?
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Then male: female ratio will not be 2.5. So, this is a wrong choice.
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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=$(\frac{New value-Old value}{old value})*100$

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

140 %
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%

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