Question

# In a seminar, the number of participants in Hindi, English and Mathematics are $$60,\ 84$$ and $$108$$ respectively. Find the 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.

Solution

## The number of participants in each room must be the $$HCF$$ of $$60,84$$ and $$108$$.In order to find the $$HCF$$ of $$60,84$$ and $$108$$, we first the $$HCF$$ of $$60$$ and $$84$$ by Euclids division algorithm:Clearly, $$HCF$$ of $$60$$ and $$84$$ is $$12$$.Now, we find the $$HCF$$ of $$12$$ and $$108$$Clearly, $$HCF$$ of $$12$$ and $$108$$ is $$12$$.Hence, the $$HCF$$ of $$60,84$$ and $$108$$ is $$12$$.Therefore, in each room maximum $$12$$ participants can be seated.Wehave,Total number of participants $$=60+84+108=252$$$$\therefore \quad$$ Number of rooms required $$=\dfrac { 252 }{ 12 } =21$$.Mathematics

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