Question

The ratio of boys to girls at a college is $4$:$5$. How many boys and girls are there if the total number of students is $3321$?

Answer 1

Hint: In this question, they have given the ratio of boys and girls in the college and total number of students in the college. We are asked to find the total number of boys and girls in the college. Since they have given the ratio and the total, we will find the total number of boys and girls by multiplying the ratio to the total number and dividing the sum of ratios.

Complete Step by Step Solution:
The given ratio of boys to girls at a college is $4$:$5$ and the total number of students in the college is $3321$. We need to find the total number of boys and girls in the college.
According to the question,
\[ \Rightarrow \dfrac{4}{5} = \dfrac{{{\text{boys}}}}{{{\text{girls}}}}\]
The total includes both the boys and girls.
Therefore total number of boys in the college = $3321 \times \dfrac{4}{9}$
$ \Rightarrow \dfrac{{13284}}{9}$
$ \Rightarrow 1476$
And the total number of girls in the college = $3321 \times \dfrac{5}{9}$
$ \Rightarrow \dfrac{{16605}}{9}$
$ \Rightarrow 1845$

Therefore the total number of boys and girls in the college is $1476$ and $1845$ respectively

Note: Ratio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of\[a:b\] , then it is a ratio whereas a proportion states that two ratios are equal. We can say that the comparison or simplified form of two quantities of the same kind is referred to as ratio. The sign used to denote a ratio is ‘:’
Important points:
The ratio should exist between the quantities of the same kind
While comparing two things, the units should be similar
There should be significant order of terms
The comparison of two ratios can be performed, if the ratios are equivalent like the fractions