Question

In a class, the number of girls is 20% more than that of boys. The strength of the class is 66. If 4 more girls are admitted to the class, what will be the ratio of the number of boys to that of the girls?
A. \[3:4\]
B. \[5:2\]
C. \[1:3\]
D. \[2:7\]

Answer 1

Hint: First of all, consider the number of boys to a variable and then find the number of girls in terms of the same variable and equal their sum to the total strength of the class so that we can find the total number of boys and girls. Then add 4 more girls to the total number of girls and then find the ratio of the number of boys to girls to get the required answer.

Complete step by step solution:
Let the number of boys be \[x\].
Given that girls are 20% more than the number of boys.
Now 20% of \[x = \dfrac{{20}}{{100}} \times x = \dfrac{x}{5}\]
Thus, the number of girls is equal to \[x + \dfrac{x}{5} = \dfrac{{6x}}{5}\]
Also, given that the strength of the class i.e., the total number of the boys and girls are 66.
\[
   \Rightarrow x + \dfrac{{6x}}{5} = 66 \\
   \Rightarrow \dfrac{{11x}}{5} = 66 \\
  \therefore x = \dfrac{{66 \times 5}}{{11}} = 30 \\
\]
So, the number of boys is \[x = 30\] and the number of girls is \[\dfrac{{6x}}{5} = \dfrac{{6 \times 30}}{5} = 36\].
If 4 more girls are added then the number of girls is 36 + 4 = 40.
So, the ratio of numbers boys to girls \[ = 30:40 = 3:4\].
Thus, the correct option is A. \[3:4\]

Note: As girls are 20% than the boys, the obtained number of girls should be more than that of the boys. \[x\% \] of \[y\] is given by \[\dfrac{x}{y} \times 100\]. Also. Check that the required ratio is in proper fraction or not. It should be in the proper fraction as the number of girls are more than that of the boys.