National Art convention got registrations from students from . . .

Question : National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested in the same artform and the number of students in each group is the same. Find the number of students in each group. Find the number of groups in each art form. How many rooms are required if each group will be allotted a room?

Doubt by Swarna 

Solution : 

The numbers of students interested in each art form are:

Music: 60

Dance: 84

Handicrafts: 108

We'll find the HCF of these numbers:

60=2²×3×5

84=2²×3×7

108=2²×3³
HCF = 2²×3
HCF = 4×3
HCF = 12

So, the maximum number of students we can have in each group is 12.

Now, let's find the number of groups in each art form:

Music: Number of groups = 60 / 12 = 5 groups

Dance: Number of groups = 84 / 12 = 7 groups

Handicrafts: Number of groups = 108 / 12 = 9 groups

Now, to find out how many rooms will be required, we need to add up the total number of groups across all art forms.

Total number of groups = 5 (music groups) + 7 (dance groups) + 9 (handicraft groups) = 21 groups

Therefore, 21 rooms will be required if each group is allotted a room.

Similar Question : 
National art convention centre got registration from students from all part of the country. 60 are interested in music, 84 are interested in dance and 100 students are interested in handicraft. For optimum cultural exchange, the organisers wish to keep minimum number of groups such that each group consisted of students interested in same art and number of students in each group is the same. Find out the number of students in each group. How many rooms will be required if each group is allotted a room?