Question

The ratio of boys to girls in the class is \[{\text{2:3}}\]. If \[{\text{20 % }}\]of boys leaves this class , than new ratio of boys to girls is
A.\[{\text{8:15}}\]
B.\[{\text{8:3}}\]
C.\[3:7\]
D.\[4:7\]

Answer 1

Hint: Let the number of boys be x and the number of girls be y . And then calculate the new number of boys and finally obtain the ratio of the number of boys and girls.

Complete step-by-step answer:
Let the number of boys be x
Let the number of girls be y
Now , as per the given x : y is \[{\text{2:3}}\] , using this , we get,
\[
   \Rightarrow \dfrac{{\text{x}}}{{\text{y}}}{\text{ = }}\dfrac{{\text{2}}}{{\text{3}}} \\
   \Rightarrow {\text{3x = 2y}} \\
\]
Now , \[{\text{20 % }}\] of boys leave the class it means mathematically this can be expressed as
\[
   \Rightarrow {\text{x - }}\dfrac{{{\text{20x}}}}{{{\text{100}}}} \\
   \Rightarrow {\text{x - }}\dfrac{{\text{x}}}{{\text{5}}} \\
   \Rightarrow \dfrac{{{\text{4x}}}}{{\text{5}}} \\
 \]
Now the new number of boys in the class \[{\text{ = }}\dfrac{{{\text{4x}}}}{{\text{5}}}\]
And the number of girls in the class is y
So the new ratio of boys to girls is
\[
   \Rightarrow \dfrac{{\dfrac{{{\text{4x}}}}{{\text{5}}}}}{{\text{y}}} \\
   \Rightarrow \dfrac{{{\text{4x}}}}{{{\text{5y}}}} \\
 \]
As we know that x : y is \[{\text{2:3}}\] using this in the above equation
\[
   \Rightarrow \dfrac{{\text{4}}}{{\text{5}}}{\text{(}}\dfrac{{\text{x}}}{{\text{y}}}{\text{)}} \\
   \Rightarrow \dfrac{{\text{4}}}{{\text{5}}}{\text{(}}\dfrac{{\text{2}}}{{\text{3}}}{\text{)}} \\
   \Rightarrow \dfrac{{\text{8}}}{{{\text{15}}}} \\
 \]
Hence , option (a) is the correct answer.


Note: A ratio is a way to compare two quantities by using division as in miles per hour where we compare miles and hours. A proportion on the other hand is an equation that says that two ratios are equivalent. If one number in a proportion is unknown you can find that number by solving the proportion.