Question

The number of boys and girls in a class is in the ratio 8 : 5. The number of boys is 9 more than the number of girls. The total number of students in the class is​

Answer 1

Given: The number of Boys and Girls in a Class is in the ratio of 8 : 5. & The number of Boys is 9 more than the number of Girls.

Need to find: The Total number of Students?

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❍ Let's say, that the number of present Boys and Girls in the class be 8x and 5x respectively.

⠀

$\underline{\maltese\:\boldsymbol{According\;to\;the\; Question\;:}}$⠀⠀

• It is given that, the number of Boys in the class is 9 more than the number of Girls in the Class.

⠀

$:\implies\sf \Big\{No.\; of\;Boys\Big\}=\Big\{No.\;of\;Girls+9\Big\}$

$:\implies\sf 8x = 5x + 9$

$:\implies\sf 8x - 5x = 9$

$:\implies\sf 3x = 9$

$:\implies\sf x = \cancel\dfrac{9}{3}$

$:\implies\underline{\boxed{\pmb{\frak{\purple{x = 3}}}}}\;\bigstar$

⠀

Therefore,

• Number of Girls, 5x = 5(3) = 15
• Number of Boys, 8x = 8(3) = 24

∴ Hence, total number of Boys and Girls are 15 and 24 respectively.

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• T o t a l⠀n o.⠀o f⠀S t u d e n t s :

➟ No. of Students = No. of Boys + No. of Girls

➟ No. of Students = 15 + 24

➟ No. of Students = 39

⠀

$\therefore{\underline{\textsf{Hence, total number of students in the class are \textbf{39}.}}}$

Answer 2

Let

• Number of boys=8x
• Number of girls=5x

ATQ

$\\ \sf\longmapsto 8x=5x+9$

• take 5x to left side

$\\ \sf\longmapsto 8x-5x=9$

$\\ \sf\longmapsto 3x=9$

• Take 3 to right side

$\\ \sf\longmapsto x=\dfrac{9}{3}$

$\\ \sf\longmapsto x=3$

Now

$\\ \sf\longmapsto Number\:of\:Boys=8x=8(3)=24$

$\\ \sf\longmapsto Number\:of\:Girls=5x=5(3)=15$

Strength of class:-

$\\ \sf\longmapsto Number\:of\:boys+Number\:of\:Girls$

$\\ \sf\longmapsto 24+15$

$\\ \sf\longmapsto 39$

There are total 39 students in class.