Question

In a seminar, the number of participants for the subjects 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 are for the same subject.

• A. 7
• B. 14
• C. 21
• D. 28

Answer 1

The correct option is C 21

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

In each room, the same number of participants are to be seated and all of them must be for the same subject.

$\therefore$ Number of participants in each room must be the HCF of 60, 84 and 108.

Prime factorisation of 60, 84 and 108:
$60=2^2\times 3\times 5$
$84=2^2\times 3\times 7$
$108=2^2\times 3^3$

$\therefore$ HCF $=2^2\times 3=12$

In each room, 12 participants can be accommodated.

$\text{Number of rooms}=\frac{\text{Total number of participants}}{12}$
$=\frac{60+84+108}{12}$
$=\frac{252}{12}$
$=21$

$\therefore$ The total number of rooms is 21.