Question

Schools have a recommended students-teacher ratio as $35:1$. Next year, school expects an increase in enrolment by $280$ students. How many new teachers will they have to appoint to maintain the students-teacher ratio?

Answer 1

To maintain the student teacher ratio as $35:1$, the number of teachers appointed will be in proportion with the additional $280$ students.

In other words, one teacher is appointed on $35$ students. Now the number of students has increased by $280$. So, the number of teachers will also increase.

Hence, the number of students ($s$) and number of teachers ($t$) are directly proportional to each other.

$\Rightarrow \frac{s}{t}=constant$

Let, for $280$ students, the number of teachers to be appointed be $x$.
$\Rightarrow \frac{s_1}{t_1}=\frac{s_2}{t_2}$
$\Rightarrow \frac{35}{1}=\frac{280}{t_2}$
$\Rightarrow t_2=\frac{280}{35}=8$

Therefore with the addition of $280$ students, $8$ additional teachers have to be appointed.