Question

In a school, 3/ 5 of the total students are girls , if the number of girls is 120 more than that of the boys , what is the strength of the school ? How many boys are there ?​

Answer 1

Answer:

We know that:

35x is the number of girls in the class

24 is the number of boys in the class.

With our assumptions, we can determine that x−35x=24

Therefore, 25x=24

x=60

Answer 2

☯GIVEN :

• $\bf {\dfrac{3}{5}}$ of the total students are girls.

• The number of girls is 120 more than that of the boys.

☯ TO FIND :

• Strength of the school.

• The number of boys.

➲SOLUTION :

Let the strength of the school be x.

Then, the number of girls = $\sf{x \times \dfrac{3}{5}} = \bf{\dfrac{3x}{5}}$

The number of boys :

$\to \sf {x - \dfrac{3x}{5}}$

$\to \sf {\dfrac{5x-3x}{5}}$

$\to \bf {\dfrac{2x}{5}}$

✞We know that,

• The number of girls is 120 more than that of the boys.

▪According To The Question :

$: \implies{ \sf{ \dfrac{3x}{5} = \dfrac{2x}{5} +120}}$

• Transposing $\bf {\dfrac{2x}{5}}$ to LHS by changing sign.

$: \implies{ \sf{ \dfrac{3x}{5} - \dfrac{2x}{5} = 120}}$

$: \implies{ \sf{ \dfrac{3x - 2x}{5} = 120}}$

$: \implies{ \sf{ \dfrac{x}{5} = 120}}$

• By cross multiplication :

$: \implies{ \sf{x = 120 \times 5}}$

$: \implies{ \underline { \huge{\boxed{ \purple {\bf{600}}}}}}$

★ Strength of the school :

• x = 600

★ The number of boys :

$\leadsto \sf {\dfrac{2x}{5}}$

$\leadsto \sf {\dfrac{2 \times 600}{5}}$

$\leadsto \sf { \cancel{\dfrac{1200}{5}}}$

$\leadsto \underline{\boxed{ \green{\bf {240}}}}$

• ✞Final Answer :

$\huge{ \blue{ \therefore}}$ Strength of the school = 600

$\huge{ \pink{ \therefore}}$The number of boys = 240