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Q.

In a seminar, the number of participants in Hindi, English and mathematics are 60, 84 and 108 respectively. Find the minimum number of rooms required, if in each room, the same numbers of participants are to be seated and all of them being in the same subject.

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a

21

b

14

c

22

d

25

answer is A.

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Detailed Solution

Given is that a seminar has the number of participants in Hindi, English and mathematics as 60, 84 and 108 respectively.
We have to determine the minimum number of rooms in which participants will be seated, given that the same number of participants are there in each room.
The total number of participants that will be present in each room is the number which will divide each of the given numbers of students i.e., 60, 84 and 108. That will be the HCF of these numbers.
So, the prime factorization of 60, 84 and 108 is as follows,

60 = 2 × 2 × 3 × 5 84 = 2 × 2 × 3 × 7 108 = 2 × 2 × 3 × 3 × 3

H.C.F of 60,84,108
=

22 × 3 = 12

So, the total number of participants seated in each of the rooms is found as 12.
Now, the total number of rooms with 12 participants each will be,

= 60 + 84 + 108 12 = 25212 = 21

Therefore, the minimum number of rooms required for the participants of the seminar is found as 21.
Hence, the correct option is (1).

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