Question

The ratio of boys to girls in a class is \[2:3\]. If \[20\% \] of boys leave this class, then the new ratio of boys to girls is
A.\[8:15\]
B.\[8:3\]
C.\[3:7\]
D.\[4:7\]

Answer 1

Hint: Here, we will find the ratio to find the total number of outcomes. Then we will find the number of boys by multiplying 100 with the fraction for boys \[\dfrac{2}{5}\] and the number of girls by multiplying 100 with the fraction for girls \[\dfrac{3}{5}\]. Then we will subtract it from 100 to find the number of boys stayed in the class and multiply the number with the number of boys.

Complete step-by-step answer:
We are given that the ratio of boys to girls in a class is \[2:3\].
Adding the ratio to find the total number of outcomes, we get
\[ \Rightarrow 2 + 3 = 5\]
We will find the number of boys by multiplying 100 with the fraction for boys \[\dfrac{2}{5}\], we get
\[ \Rightarrow \dfrac{2}{5} \times 100 = 40\]
Now we will find the number of girls by multiplying 100 with the fraction for girls \[\dfrac{3}{5}\], we get
\[ \Rightarrow \dfrac{3}{5} \times 100 = 60\]
If \[20\% \] of boys leave this class, then we will subtract it from 100 to find the number of boys stayed in the class, we get
\[
   \Rightarrow \left( {100 - 20} \right)\% \\
   \Rightarrow 80\% \\
 \]
Multiplying the above number with number of boys, we get
\[
   \Rightarrow \dfrac{{80}}{{100}} \times 40 \\
   \Rightarrow 32 \\
 \]
Thus, there are 32 boys in the class now.
Dividing the 32 boys by 60 girls to find the required ratio, we get
\[
   \Rightarrow \dfrac{{32}}{{60}} \\
   \Rightarrow \dfrac{8}{{15}} \\
 \]
Therefore, the required ratio is \[8:15\].
Hence, option A is correct.

Note: We will add the number of boys and girls to find the total number of students. One needs to assume the boys and girls have the same variables or else the answer will be wrong. We can also verify our answer by taking the ratio, \[32:60\]. So we have to simplify the obtained ratio, we get
$\Rightarrow$ \[\dfrac{{{{{{32}}}{{{{{}}}}}}}}{{{{{{60}}}{{{{{}}}{}}}}}} = \dfrac{8}{{15}}\]
Hence, our answer is correct.