Question

There was a seminar in a school , the number of participants in Mathematics, Physics and Chemistry are 60, 96 and 144 respectively. Teacher want to find out the number of rooms required so that maximum participants will sit in a particular room.Teacher took help of her friend Ria, a maths teacher for the same. What do you think her friend Ria answered.

Answer 1

Answer:

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