Question

The ratio of boys to girls in a class is \[3:2\]. If the number of boys is 6 more than the number of girls. Find the number of girls and the total strength.

Answer 1

Hint: Take the number of boys to be \[3k\] and the number of girls to be \[2k\]. Form an equation for the second half of the question. Find the value of \[k\] and substitute the value in \[2k\]. To find the strength of the class find the sum of the number of boys and the number of girls.

Complete step by step solution:Let the number of boys be \[3k\] and the number of girls be \[2k\] .
According to the question; “the number of boys is \[6\] more than number of girls”; let us put this statement into an equation form;
The number of boys=\[6\](more)+number of girls; (let us substitute the values);
\[3k = 6 + 2k\] (Now solve this equation for k);
\[\begin{align}
  3k = 6 + 2k
 \Rightarrow 3k - 2k = 6
  \Rightarrow k = 6
\end{align} \]
Now to find the number of girls we can substitute the value of “\[k\]” in “\[2k\]”;
Therefore the number of the girls\[ = 2k\]
                                                            \[ = 2 \times 6 = 12\]
Therefore the number of girls is \[12\].
To find the total strength of the class we need to find the number of boys in the class as well; so let us substitute the value of \[k\] in \[3k\] as well;
Number of the boys\[ = 3k\]
                                    \[ = 3 \times 6 = 18\]
Therefore the number of boys is \[18\].
Now the total strength of the class will be\[ = \] number of the boys+number of the girls
                                                                          \[ = 12 + 16 = 30\]

Therefore the number of students is \[30\].

Note: In the question; the number of boys were said to be 6 times “more” than the number of girls; so we add up the values in case of “more” number of people. The concepts of ratios and proportion should be clear by the student. This type of questions are quite easy and scoring, students should not miss out on practicing such types of questions just because they are easy, remember; sometimes you might just forget the simplest steps.