Question

Q1-in a seminar the number of participants in hindi, English and mathematics are 60,84 and 108, respectively. The minimum number of rooms, required if in each room the same number of participants at to be seated and all of them being in the same subject?

Answer 1

the number of participants in each room must be the HCF of 60, 84 and 108.
so by euclid's division lemma,
108= 84*1+24
84= 24*3+12
24=12*2
therefore, the hcf of 108 and 84 is 12.
similarly the hcf of 60 and 84 will be 12.

therefore in each room, 12 members can sit.
total number of participants
= 60+84+108
=252
munber of rooms required=
total students/number of students in one room
= 252/12
=21
therefore 21 rooms are required.