Question

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 are to be seated and all of them being in the same subject?
$A$ 21
$B$ 42
$C$ 12
$D$ 24

Answer 1

Hint- According to this question, we should concentrate on the fact that each room accommodates the maximum number of participants so that minimum rooms will be used. We will use the concept of highest common factor to arrange the maximum number of students.

Complete step-by-step answer:
$ \Rightarrow $ HCF of 60, 84 and 108
 Firstly, we will do the Prime factorisations of 60, 84 and 108.
$ \Rightarrow $60 = 3$ \times $4$ \times $5
$ \Rightarrow $84 = 3$ \times $4$ \times $7
$ \Rightarrow $108 = 2$ \times $2$ \times $3$ \times $3
$ \Rightarrow $HCF of 60, 84 and 108 is 3 $ \times $ 4 = 12
Now we will find the total number of students
$ \Rightarrow $60 + 84 + 108
$ \Rightarrow $252
Further in order to calculate minimum rooms for accommodating maximum students
We will divide total number of students by HCF of 60, 84 and 108
$ \Rightarrow $$\dfrac{{252}}{{12}}$
$ \Rightarrow $21
Hence 21 rooms will be used to accommodate 252 students.
$\therefore $Option C is right.

Note- We should know the concept of highest common factor to solve maximum related problems. Also one can get confused with LCM and HCF, so we should learn the difference between maximum and minimum related problems. For minimum, we should use LCM and for maximum, we should use HCF. Hence we will get the desired result.