Question

In a college, the ratio of the number of boys to girls is $8:5$. If there are $200$ girls, the total number of students in the college is
A. $420$
B. $520$
C. $620$
D. $720$

Answer 1

Hint: Use the property of ratio to express the number of girls and boys as $5x$ and $8x$ respectively. Then using the given data to find the number value of $x$, using the value of $x$, we can easily find the number of boys in the college.

Complete answer:
It is given in the problem that the ratio of the number of boys to girls is $8:5$ and it is also given that there are $200$ girls in the college.
The goal of the problem is to find the total number of students in the college.
First of all, assume $x$ be any number such that the number of girls and boys are given as:
Number of girls$ = 5x$;
Number of boys$ = 8x$
But there are $200$ girls in the college, so from the above we have
$200 = 5x$
Solve this equation form the value of $x$:
$ \Rightarrow x = \dfrac{{200}}{5}$
$ \Rightarrow x = 40$
The value of $x$ is $40$. Now, use this value to find the number of boys in the college.
We have the assumed value of the number of boys in the college as:
Number of boys$ = 8x$;
Put the value of $x$ in the above equation:
Number of boys$ = 8\left( {40} \right)$
Number of boys$ = 320$
Therefore, there are $320$ boys in the college.
We know that the total number of the students can be obtained by adding total number of girls and total number of boys in the college. That is,
Total number of students$ = \left( {{\text{Number of boys}}} \right) + \left( {{\text{Number of girls}}} \right)$
There are $320$ boys and $200$ girls in the college, then the total number of students becomes
Total number of students$ = \left( {320} \right) + \left( {{\text{200}}} \right)$
Total number of students$ = 520$
Therefore, there are $520$ students in the college.


Note: We have given the ratio of the number of boys and the number of girls, as $8:5$. It means that there exists a common divisor of $8$ and $5$, which is assumed as $x$ to precede the calculation.