Question

The number of participants in Hindi, English, and math quiz are $60,84,$ and $108$ respectively. Find the minimum number of rooms required if in each room the same number of participants of the same subject is seated.

Answer 1

Step 1: Finding the number of participants in each room:

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.

Prime factorisations of $60=2\times 2\times 3\times 5$

Prime factorisations of $84=2\times 2\times 3\times 7$

Prime factorisations of $108=2\times 2\times 3\times 3\times 3$
HCF of $60,84,$ and $108$ is $2\times 2\times 3=12$

Therefore, in each room $12$ participants can be seated.

Step 2: Finding the number of rooms required:

Number of rooms required$=$Total number of participants$÷12$.

$=\frac{(60+84+108)}{12}$

$=\frac{252}{12}$

$=21$

Therefore, the total number of rooms is $21$.

Hence, in each room $12$ participants can be seated and the total number of rooms required is $21$.