Question

In the two rooms of Family Restaurant, Number of people sitting around each table in both rooms must be equal. A maximum of 54 people can sit in the first room and 36 people in the second. How many maximum chairs can be around each table?

• A. $18$
• B. $12$
• C. $20$
• D. $8$

Answer 1

The correct option is A $18$

Maximum people sit in first room $=54$
Maximum people sit in second room $=36$
Given that, Number of people sitting around each table in both rooms must be equal.
So, maximum possible chairs that can be arranged around each table for the people will be GCD of $54$ and $36$.
$54=2\times 3\times 3\times 3$
$36=2\times 2\times 3\times 3$
GCD of $54$ and $36$ is $2\times 3\times 3=18$

So, Maximum $18$ chairs will be around each table.