Question

In a school,4/5 of the students are boys and the number of girls is 100. Find the number of boys.
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Answer 1

Answer:

400

Step-by-step explanation:

As per the próvídéd information in the given question, we have :

• In school, 4/5 of the students are boys and the number of girls is 100.

We are asked to calculate the number of boys.

Firstly, let's assume the total number of students as x.

According to the question :

$\longmapsto \rm {Number_{(Boys)} = \dfrac{4}{5} \times Number_{(Students)} }$

$\longmapsto \rm {Number_{(Boys)} = \dfrac{4}{5}x \dots (1)}$

In order to find the number of boys, we need to calculate the total number of students first.

So, also as per the question :

$\longmapsto \rm {Number_{(Students)} = Number_{(Boys)} + Number_{(Gir{l}s)} }$

Substituting the values as per the assumption we had.

$\longmapsto \rm {x =\dfrac{4}{5}x +100 }$

Taking the LCM and símplífyíñg further.

$\longmapsto \rm {x =\dfrac{4x + 500}{5}}$

Transposing 5 from R.H.S to L.H.S, the áríthmétíc operator will be changed.

$\longmapsto \rm {5x =4x + 500}$

Transposing 4x from R.H.S to L.H.S, its sign will get changed.

$\longmapsto \rm {5x - 4x = 500}$

Pérfórmíñg subtraction in L.H.S.

$\longmapsto \bf {x = 500}$

∴ Total number of students is 500.

Now, substitute the values of x in the equation 1 in order to calculate the number of boys.

$\longmapsto \rm {Number_{(Boys)} = \dfrac{4}{5}x \dots (1)}$

$\longmapsto \rm {Number_{(Boys)} = \dfrac{4}{5} \times 500 }$

Substituting the value of x.

$\longmapsto \rm {Number_{(Boys)} =4 \times 100 }$

Símplífyíñg further by pérfórmíñg division.

$\longmapsto \bf {Number_{(Boys)} =400 }$

Pérfórmíñg multiplication.

∴ Total number of boys is 400.