Question

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 number of participants are to be seated and all of them being in the same subject. [4 MARKS]

Answer 1

Concept : 1 Mark
Application : 2 Marks
Conclusion : 1 Mark

It is given that, each room the same number of participants are to be seated and all of them must be of the same subject.

The number of rooms will be minimum if each room accomodates maximum number of participants.

$\therefore$ 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,

$60=2^2\times 3\times 5$

$84=2^2\times 3\times 7$

$108=2^2\times 3^2$

$\therefore$ HCF of 60, 84 and 108 is $2^2\times 3=12$

Therefore, in each room 12 participants can be seated.

$\therefore Numberofroomsrequired=\frac{Totalnumberofparticipants}{12}$

$=\frac{60+84+108}{12}=\frac{252}{12}=21$