Question

Girls are 46% of the total number of the students in the school. Find the ratio of the number of girls to the number of boys.

Answer 1

Hint: Think of the basic definition of ratio and use the fractional form of a ratio to find the answer to the above question. Let the total number of students in the school be x.

Complete step-by-step solution -
Let us first know what a ratio is.
A ratio in basic words is a quantity used to define a comparison between two quantities. A bit toward the advanced side, it is the quantity that defines how many times of one quantity is that of others.
 At our level, apart from the definition, we will treat it as a simple fraction that defines a relation between two given quantities.
Now, starting with the solution to the above question. Let the total number of students in the school be x. Now it is given that 46% of the total students in the school are girls.
$\therefore \text{number of girls = }\dfrac{46}{100}\times x$
Also, we know that the students in the school are either girls or boys. So, we can deduce that 54% of the students in the school are boys.
$\therefore \text{number of boys = }\dfrac{54}{100}\times x$
If we divide the above two equations, we get
$\dfrac{\text{number of girls}}{\text{number of boys}}\text{ = }\dfrac{\dfrac{46}{100}\times x}{\dfrac{54}{100}\times x}=\dfrac{46}{54}=\dfrac{23}{27}$
Therefore, the ratio of the number of girls to the number of boys is 23:27.

Note: Read the question carefully as in the question, including ratio, there is always a chance that the question might have a twist hidden in the words of the question. Also, while solving a fraction for finding the ratio, be sure that you convert it to the simplest form, i.e., the numerator and the denominator must not have any common factors.