Question

In a delegation of students there are 60 Indian, 84 Chinese and 108 British. They all want
to study in the same hotel. The number of students stay in each room is same and will
also stay with their own country students. Find minimum number of rooms required for
stay of these students.

Answer 1

Step-by-step explanation:

The Number of room will be minimum if each room accomodates maximum

number of participants. Since in each room the same number of participants

are to be seated and all of them must be of the same subject. Therefore, the

number of participants in each room must be the HCF of 60,84 and

108. The prime factorisations of 60,84 and 108 are as under.

60=2

2

×3×5,84=2

2

×3×7 and 108=2

2

×3

3

∴ HCF of 60,84 and 108 is 2

2

×3=12

Therefore, in each room 12 participants can be seated.

∴ Number of rooms required=

12

Total number of participants

=

12

60+84+108

=

12

252

=21