Question

the ratio of boys to girls in a school is 3 : 4
there are 120 more girls than boys
how many students are there in the school

Answer 1

Given :

$\sf \: The \: ratio \: of \: boys \: to \: girls \: in \: a \: school \: is \: 3:4 .$

$\sf \: There \: are \: 120 \: more \: girls \: than \: boys.$

To Find :

$\sf \: We \: have \: to \: find \: the \: total \: number \: of \: students.$

So, Let's Start :

Let us just assume that no. of Boys be 3M and no. of Girls be 4M.

There are 120 more girls than boys.

$\sf \: As \: per \: the \: calculation :$

$\sf \: \implies{4M \: = \: 120 \: + \: 3M}$

$\sf \: \implies\sf {4M-3M\:=\:120}$

$\sf \: \implies{M\:=\:120}$

$\sf \: Therefore,$

$\sf \: Number \: of \: Boys \: = \: 3M \: = \: 3(120) \: = \: 360$

$\sf \: Number \: of \: Girls \: = \: 4M \: = \: 4(120) \: = \: 480$

To find the total number of students in the school, We have to add the both number of boys and girls.

$\sf \: Total \: No. \: of \: Students \: = \: No. \: of \: Girls \: + \: No. \: of \: Boys.$

$\sf \: \implies{360 + 480} \: = \: 840$

$\sf \: So, \:Total \: No. \: of \: Students \: = 840.$

Answer 2

$\huge\underline{\underline\mathtt\color{pink}question}$

The ratio of boys to girls in a school is 3 : 4. There are 120 more girls than boys. How many students are there in the school?

${\dag\:{\underline{\boxed{\mathfrak{\purple{Answer}}}}}}$

Given:-

• Ratio of boy : girl is 3:4
• girls = 120 + boys

____________________

To find:-

• Number of students in the school

____________________

➪ Let value of ratio be K.

➪ So the ratio of girl will be 4K and ratio of boy will be 3K.

➪ According to the question the equation will be

• 4K = 120 + 3K

➪ 4K - 3K = 120

➪ K = 120

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➦ So the value for K is 120.

• Let us put the value of K in equation.

➮ So for girls it is 4K

➮ 4(120) = 480

➮ For boys it is 3K

➮ 3(120) = 360

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So there are 480 girls and 360 boys in the school.

Verification:-

• 4K = 120 + 3K
• 480 = 120 + 360