Question

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

Answer 1

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

$\small{\sf{\:\:\:\:\:\:\:\:\:\:\:\: Assumption}}$

Let us assume that the number of boys be 3M and number of girls be 4M.

There are 120 more girls than boys.

$\small{\sf{\:\:\:\:\:\:\:\:\:\:\:\: As\:per\:given\:condition}}$

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

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

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

Therefore,

Number of Boys = 3M = 3(120) = 360

Number of Girls = 4M = 4(120) = 480

To find the total number of students in the school. Add the both number of boys and girls.

i.e.

Number of students = Number of Boys + Number of Girls

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

$\rule{200}2$

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

$\small{\sf{\:\:\:\:\:\:\:\:\:\:\:\: As\:per\:given\:condition}}$

$\implies\:\sf{\dfrac{Boy}{Girl}\:=\:\dfrac{3}{4}}$

$\implies\:\sf{\frac{B}{G}\:=\:\frac{3}{4}}$

$\implies\:\sf{B\:=\:\frac{3G}{4}}$

There are 120 more girls than boys.

$\small{\sf{\:\:\:\:\:\:\:\:\:\:\:\: As\:per\:given\:condition}}$

$\implies\:\sf{G\:=\:120+B}$

$\implies\:\sf{G-B\:=\:120}$

Substitute value of B above

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

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

$\implies\:\sf{G\:=\:4(120)\:=\:480}$

Substitute value of G in B

$\implies\:\sf{B\:=\:\frac{3(480)}{4}}$

$\implies\:\sf{B\:=\:3(120)}$

$\implies\:\sf{B\:=\:360}$

Total number of students = Number of Boys + Number of Girls

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

Therefore,

Total number of students in the school is 840.

Answer 2

Given :-

• Ratio of Boys : Girls = 3: 4
• Girls More Than Boys = 120 .

Solution :-

Since Ratio of Boys and Girls is 3:4 . Lets Assume That, Their are 3x boys and 4x Girls in The school ..

So,

A/q,

→ (4x - 3x) = 120

→ x = 120

So,

→ Total Number of Boys = 3x = 3*120 = 360

→ Total Number of Girls = 4x = 4*120 = 480

→ Total Students in School = Total boys + Total girls = 360 + 480 = 840 . (Ans).

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Ratio Method :-

→ Boys : Girls = 3 : 4

→ Difference b/w Ratio = (4 - 3) = 1 unit.

So,

→ 1 unit = 120

→ 7 unit = 120*7 = 840 = Total Students . (Ans).

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