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: Assume total number of students as $x$. By using the definition of percentage. After getting total, find the relation between total and the number of boys. From this relation find the number of boys which is the required result.

Complete step by step solution:
Given percentage of girls in total in the question as:
$60\%$ of total are girls.
Given the value of above percentage is equal to as: 18
Let us assume the total number of students as $x$:
x= total number of students.
So, by first 2 conditions, we get an equation as:
$60\%$ of $x\,=18........(i)$
We need a value of 60% of x to solve this.
By definition of percentage, we can say value of percentage is:
$60\%$ of $x=\dfrac{60\times x}{100}$
By cancelling numerator and denominator by 10, we get:
$60\%$ of $x=\dfrac{6\times x}{10}$
By cancelling the right hand-side, by 2, we get it as:
$60\%$ of $x=\dfrac{3x}{5}$
By substituting this in the equation (i), we get it as:
$\dfrac{3x}{5}=18$
By multiplying 5 on both the sides, we get it as:
$\dfrac{3x}{5}\times 5=18\times 5$
By simplifying the above equation, we can write it as:
$3x=18\times 5$
By simplifying the right hand-side of equation:
$3x=90$
By dividing with 3 on both sides, we get it as:
$\dfrac{3x}{3}=\dfrac{90}{3}$
By simplifying the above equation, we get it as:
$x=30.........(ii)$
We know that total is formed by boys, girls. So, total number of students = number of boys + number of girls. For equation (ii) and value of girls given, we get it as:
30=number of boys+18
Number of boys $= 30-18$
On simplification, we get
Number of boys $= 12$
Therefore, the number of boys in class is 12.

Note: Alternate ways is as 60% are girls, 40% will be boys after finding total, find 40% of total by this method also you get the same result. While taking the equation of girls be careful as it is the only main point of the solution. After that, the number of boys is found from the same number.