Question

The ratio of the boys to girls in a school is 3 : 5. If the total number of students in the school is 1800, find the number of boys and girls in the school

Answer 1

Given :

• Boys : Girls = 3:5
• Total number of students = 1800

Let :

• Number of boys = x
• Number of girls = y

To find :

• Number of boys
• Number of girls

Solution :

$\sf \: x : y \: = \:3 : 5 \\ \\ \sf \implies \: \dfrac{x}{y} = \dfrac{3}{5} \\ \sf \implies \: x \: = \dfrac{3}{5} y \: ..........equation1$

Also,

x + y = 1800

Putting value of x from equation 1, we get;

$\sf \implies \dfrac{3}{5} y \: + y = 1800 \\ \\ \sf \implies \: \frac{3 + (1 \times 5)}{5} y = 1800 \\ \\ \sf \implies \: 8y = 1800 \times 5 \\ \\ \sf \implies \: y \: = 9000 \div 8 \\ \\ \sf \implies \: y = 1125$

putting value of y in equation 1,

=> x = (3×1125)/5

=> x = 675

ANSWER :

• Number of boys (x) = 675
• Number of girls (y) = 1125

Answer 2

Given :

Boys : Girls = 3:5

Total number of students = 1800

Let :

Number of boys = x

Number of girls = y

To find :

Number of boys

Number of girls

$\huge\underline\red{Solution:}$

$\begin{gathered} \sf \: x : y \: = \:3 : 5 \\ \\ \sf \implies \: \dfrac{x}{y} = \dfrac{3}{5} \\ \sf \implies \: x \: = \dfrac{3}{5} y \: ..........equation1\end{gathered}$

Also,

x + y = 1800

1800Putting value of x from equation 1, we get;

$\begin{gathered} \sf \implies \dfrac{3}{5} y \: + y = 1800 \\ \\ \sf \implies \: \frac{3 + (1 \times 5)}{5} y = 1800 \\ \\ \sf \implies \: 8y = 1800 \times 5 \\ \\ \sf \implies \: y \: = 9000 \div 8 \\ \\ \sf \implies \: y = 1125\end{gathered}$

y=1800

⟹ 8y=1800×5

⟹ y=9000÷8

⟹ y=1125

putting value of y in equation 1,

=> x = (3×1125)/5

=> x = 675

$\huge\underline\purple{Answer:-}$

Number of boys (x) = 675

Number of girls (y) = 1125