Question

In a class, 60% of all the students are boys. It was observed that 90 girls were present in the class on a specific day. If these girls were 75% of the entire girls, then how many boy students were present.​

Answer 1

Given :

Percent of boys in the class : 60%

Number of girls present : 90

Percent of girls present : 75%

To find :

Number of boy students in the class.

Solution :

First, we should find the total number of girls in the class.

Total number of girls :

Let the number of girls in the class be m.

$\sf \dashrightarrow 75\% \: of \: m = 90$

$\sf \dashrightarrow 75\% \times m = 90$

$\sf \dashrightarrow \dfrac{75}{100} \times m = 90$

$\sf \dashrightarrow \dfrac{3}{4} \times m = 90$

$\sf \dashrightarrow \dfrac{3m}{4} = 90$

$\sf \dashrightarrow 3m = 90 \times 4$

$\sf \dashrightarrow 3m = 360$

$\sf \dashrightarrow m = \dfrac{360}{3}$

$\sf \dashrightarrow m = 120$

Now, let's find the percent of girls in the class.

Percent of girls :

$\sf \dashrightarrow 100 - 60$

$\sf \dashrightarrow 40\%$

Now, we should find the total number of students in the class.

Total number of students :

Let the total number of students be n.

$\sf \dashrightarrow 40 \% \: of \: n = 120$

$\sf \dashrightarrow 40 \% \times n = 120$

$\sf \dashrightarrow \dfrac{40}{100} \times n = 120$

$\sf \dashrightarrow \dfrac{2}{5} \times n = 120$

$\sf\dashrightarrow \dfrac{2n}{5} = 120$

$\sf \dashrightarrow 2n = 120 \times 5$

$\sf \dashrightarrow 2n = 600$

$\sf \dashrightarrow n = \dfrac{600}{2}$

$\sf \dashrightarrow n = 300$

Now, we can find the number of boys in the school.

Total number of boys :

$\sf \dashrightarrow 300 - 120$

$\sf \dashrightarrow 180$

Hence, the total number of boys in the school are 180.