Question

the number of boys and girls in a school are 480 and 384 respectively. express the ratio of the number of boys to the number of girls in the simplest form.​

Answer 1

Given : Number of boys = 480 and Number of girls = 384.

Find : We have to find the number of boys to the number of girls.

i.e.

Number of boys : Number of girls = ?

Solution :

To find number of boys to the number of girls, we have to simply divide them.

As we have given, number of boys and girls are 480 and 384.

So,

=> $\dfrac{Number \:of\: boys}{Number\:of\:girls}\:=\:\dfrac{480}{384}$

=> $\dfrac{Number \:of\: boys}{Number\:of\:girls}\:=\:\dfrac{120}{96}$

=> $\dfrac{Number \:of\: boys}{Number\:of\:girls}\:=\:\dfrac{30}{24}$

=> $\dfrac{Number \:of\: boys}{Number\:of\:girls}\:=\:\dfrac{15}{12}$

=> $\dfrac{Number \:of\: boys}{Number\:of\:girls}\:=\:\dfrac{5}{4}$

Number of boys : Number of girls = 5 : 4.

Answer 2

$\bf{\huge{\underline{\boxed{\rm{\purple{Answer:}}}}}}$

Given :-

• Number of boys in school = 480
• Number of girls in school = 384

To find :-

• the ratio of the number of boys to the number of girls in the simplest form

Solution :-

This kind of question is completely based on simple equation, where we keep solving the given numbers by dividing the numerator and denominator by possible number.

Ratio = a : b = c : d

Converting to numerator-denominator form,

$\bf\large\frac{a}{b}$ = $\bf\large\frac{c}{d}$

Let's solve by making some assumptions.

For first case :-

Let the number of boys = c = 480

Let the number of girls = d = 384

Their ratio = c : d = 480 : 384

For second case :-

Let simplest form of ratio of number of boys : number of girls = a : b

•°• Ratio of Number of boys = a

Ratio of Number of girls = b

We need to find : $\bf\large\frac{a}{b}$

$\bf\implies$ $\bf\large\frac{a}{b}$ = $\bf\large\frac{c}{d}$

$\bf\implies$$\bf\large\frac{a}{b}$ = $\bf\large\frac{480}{384}$

On dividing by 2 on LHS,

$\bf\implies$$\bf\large\frac{a}{b}$ = $\bf\large\frac{240}{192}$

Dividing further by 2 on LHS again,

$\bf\implies$ $\bf\large\frac{a}{b}$ = $\bf\large\frac{120}{96}$

Again divide LHS by 2,

$\bf\implies$ $\bf\large\frac{a}{b}$ = $\bf\large\frac{60}{48}$

Again dividing LHS by 2,

$\bf\implies$ $\bf\large\frac{a}{b}$ = $\bf\large\frac{30}{24}$

Again divide by 2 on LHS,

$\bf\implies$ $\bf\large\frac{a}{b}$ = $\bf\large\frac{15}{12}$

Now, divide the LHS by 3,

$\bf\implies$ $\bf\large\frac{a}{b}$ = $\bf\large\frac{5}{4}$

Now, there's no common number with which we can divide the numerator and denominator, so we stop here, and this is our simplest form of ratio of number of boys : number of girls.

$\bf\implies$ $\bf\large\frac{a}{b}$ = $\bf\large\frac{5}{4}$

As per our assumptions,

a = 5

b = 4

a:b = 5 : 4

Final form :-

480 : 384 = 5 : 4