Question

In a college, the ratio of the number of boys to the number of girls is 8:5. If the number of boys is
243 more than the number of girls, then what is the fraction of the number of girls in the college to the total number of students?

Answer 1

Given: Ratio of number of boys to girls = 8:5
Now, the number of boys = 8 units.
And the number of girls = 5 units.
The number of boys is 3 units more than the number of girls.
$\Rightarrow$ 3 units = 243 = 3 x 81
1 unit = 81
Now, the total number of students in college = 8 + 5 = 13 units
$=13\times 81=\times 1053$.
Therefore, the total number of students in the college is 1053.
Number of girls = 5 units = $5\times 81=405$.
The fraction of girls in the group is $=\frac{Numberofgirls}{Totalnumberofstudents}=\frac{405}{1053}=\frac{5}{13}$