Question

In a seminar, the number of participants in English, German and Sanskrit are 45,75 and 135. Find the number of rooms required to house them, in in each room, the same number of participants are to be accommodated and thy should be of the same language.​

Answer 1

${\huge{\underline{\large{\mathbb{\green{VERIFIED \: ANSWER}}}}}}$

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.

$\tt \: 60= {2}^{2} ×3×5,84= {2}^{2} ×3×7  \\ \tt \: and \: 108= {2}^{2} × {3}^{3}$

$\tt∴ HCF of 60,84 and 108 is  \\ \tt{2}^{2} ×3=12 \: </p><p>Therefore, in \: each \: room \\ \tt  \tt 12 participants \: can \: be \: seated.$

∴ Number of rooms required=

$\tt \: \frac{total \: no. \: of \: participants}{12} \\ \\ \tt \: = \frac{60 + 84 + 108}{12} \\ \\ \tt \frac{252}{12} = 12$