Question

In a workshop, the number of teachers of English, Hindi and Science are 36, 60 and 84 respectively. Find the minimum number of rooms required if in each room the same number of teachers are to be seated and all of them being of the same subject.

Answer 1

Given number of teachers:

English = 36

Hindi = 60

Science = 84

All teachers in one room must be of the same subject, and each room must have an equal number of teachers.

So, we need to find the greatest number of teachers per room that can divide 36, 60 and 84 exactly.

This means we must find HCF (36, 60, 84).

Step 1: Find HCF:

Prime factorisation:

36 = 2² × 3²

60 = 2² × 3 × 5

84 = 2² × 3 × 7

Common factors:

2² × 3

= 4 × 3

= 12

So, HCF = 12

This means 12 teachers will be seated in each room.

Step 2: Find the number of rooms.

English = `36/12` = 3 rooms

Hindi = `60/12` = 5 rooms

Science = `84/12` = 7 rooms

Required number of rooms = 3 + 5 + 7 = 15