Question

A picnic is being planned in a school for class VII. Girls are 60% of the total number of students and are 18 in number. Find the number of boys.

Answer 1

Hint: The concept of percentages and linear equations in one variable will be used here. A linear equation in one variable has exactly one root. The percentage can be converted into fraction as-
${\text{x}}\% = \dfrac{{\text{x}}}{{100}}$

Complete step-by-step solution -
We have been given that the girls occupy 60% of the students in the class, and are 18 in number. Let us assume the total number of students in the class to be x. So, we can write that 60% of the total class is the number of girls. Mathematically,
$60\% \text{of x} = 18 $
Converting percentage into fractions we get-
$\dfrac{{60}}{{100}} \times {\text{x}} = 18 \\ $
 $\Rightarrow 0.6{\text{x}} = 18 \\ $
 $\Rightarrow {\text{x}} = \dfrac{{18}}{{0.6}} = \dfrac{{18}}{6} \times 10 = 30 \\ $
This is the strength of the total class. We need to find the number of boys. We know that the percentage of girls is 60%, so the percentage of boys is-
$100\% - 60\% = 40\%$
So the number of boys can be calculated as-
$=40\% \text{of the total strength}$
$=40\% of x$
$ = \dfrac{{40}}{{100}} \times 30 = 12$
There are 12 boys in the class. This is the required answer.

Note: In such types of questions, we assume a suitable variable, form an equation, and solve it to get an answer. We just have to read the language of the question carefully and form the equation accordingly. Also, assuming a suitable variable is important. If we assumed the total number of boys to be x, we would not get a direct relation between x and the number of girls. So, we assumed the total strength to be x.