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Q.

Many schools have a suggested student-teacher ratio as 35:1. The school anticipates a 280-student rise in enrolment the following year. How many additional teachers will be needed to keep the current student-teacher ratio?

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a

7

b

8

c

9

d

10

answer is B.

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Detailed Solution

It is given that many schools have a suggested student-teacher ratio as 35:1.
We know that if two quantities

x

and

y

vary in the same way while maintaining a constant ratio between their respective values, then the two quantities are said to be in direct proportion.
i.e.

x y = k,

where k is a constant positive number.
Given that schools suggested a student-teacher ratio as 35:1. This indicates that an increase in students will result in an increase of teachers.
So, it is a situation of direct proportion.
Question Image

Question Image

Find the desired number of teachers to be appointed.
Since, this is the situation of direct proportion, therefore, the ratio remains constant. So,

351 = 280 y 1 ⇒ y 1 = 28035 ⇒ y 1 = 8

The ratio of students to teachers will need to be maintained by hiring 8 additional teachers.
Hence, option (2) is correct.

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