Q) 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.

Q27 – Sample Question Paper – Set 1 – Maths Standard – CBSE 2026

Ans:

STEP BY STEP SOLUTION

Step 1: Since the number of teachers in a room need to be same across all 3 subjects, hence we need to take common factors of total teachers’ count across 3 subjects.

The number of rooms will be minimum if number of participants in each room are maximum. Here, maximum number of participants need to be seated in a room, therefore, we need to take highest common factor or HCF.

Hence, we will find the HCF of 36, 60 and 84

Step 2: By Prime factorisation, let’s find factors of 36, 60, 84:

36 = 2 x 2 x 3 x 3

60 = 2 x 2 x 3 x 5

84 = 2 x 2 x 3 x 7

Now the HCF will have only the common factors among all 3 numbers

Hence, the HCF is: (2 x 2 x 3) = 12

Step 3: Now a set of12 participants for each subject will occupy a room.

Therefore, total number of rooms = Rooms for English (R _E ) + Rooms for Hindi (R _H ) + Rooms for Science (R _S )

Now Rooms required for English = Teachers for English / Teachers seated in one room

∴ R _E = 36  / 12 = 3

Rooms required for Hindi = Teachers for Hindi / Teachers seated in one room

∴ R _E = 60  / 12 = 5

Rooms required for Science = Teachers for Science / Teachers seated in one room

∴ R _E = 84 / 12 = 7

∴ Total number of rooms = R _E  + R _H  + R _S

= 3 + 5 + 7 = 15

Therefore, minimum 15 rooms are required.

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