Question

In a primary school there shall be 3 teachers to 60 students. If there are 400 students enrolled in the school, how many teachers should be there in the school in the same ratio?

Answer 1

Hint: First of all use the unitary method to calculate the number of students required for 1 teacher by dividing the number of students (60) with the number of teachers (3). Take the ratio of number of teachers to the number of students in the simplified form. Now, assume that x number of teachers are required for 400 students and take the ratio of x to 400 and equate it with the ratio obtained in the previous step. Solve for the value of x to get the answer.

Complete step by step answer:
Here we have been given that for 60 students there are 3 teachers in a primary school and we are asked to calculate the number of teachers required for 400 students.
Now, number of students for 3 teachers = 60
Applying the unitary method we get,
$\Rightarrow $ Number of students for 1 teacher = $\dfrac{60}{3}$
$\Rightarrow $ Number of students for 1 teacher = 20
So, we have the simplified ratio of the number of teachers to the number of students = $1:20$.
Now, assuming that the number of teachers required for 400 students is x, we must have the ratio of number of teachers to the number of students in this case, i.e.$x:400$, equal to $1:20$, so we get,
$\Rightarrow \dfrac{x}{400}=\dfrac{1}{20}$
Solving for the value of x we get,
$\begin{align}
  & \Rightarrow x=\dfrac{400}{20} \\
 & \therefore x=20 \\
\end{align}$
Hence, the number of teachers for 400 enrolled students must be 20 in number.

Note: Note that the above question is an example of basic ratio and proportional problem and simply you may call an example of the unitary method. In proportion form we can write the expression as $1:20=x:400$ and use the theorem given as ‘product of the means is equal to the product of extremes’, where 1 and 400 are the extremes and 20 and x are the means.