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In a seminar, the number of participants in 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 being in the same subject.

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This is the basic and exam oriented question from real numbers in which we have been asked to find the minimum number of rooms required considering the same number of participants in each room if the number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.

Kindly solve the above problem in detail

RS Aggarwal, Class 10, chapter 1B, question no 18

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1. 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 theÂ HCFÂ ofÂ 60,84Â and
108. The prime factorisations ofÂ 60,84Â andÂ 108Â are as under.

60=2Â²Ã—3Ã—5, 84=2Â²Ã—3Ã—7Â andÂ 108=2Â²Ã—3Â³

âˆ´Â HCFÂ ofÂ 60,84Â andÂ 108Â isÂ 2Â²Ã—3=12
Therefore, in each roomÂ 12Â participants can be seated.

âˆ´Â NumberÂ ofÂ roomsÂ required=TotalÂ numberÂ ofÂ participants/12â€‹
=(60+84+108)/12â€‹=252â€‹/12=21

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