Question

The tables at a banquet are designed in the shape of a Pentagon and 1 shape of square. Guests are allowed to sit in each corner of the pentagonal and square table. If there are a total of 204 guests, calculate the number of pentagonal tables required if all guests fill each seat of the table?

• A. 30
• B. 35
• C. 40
• D. 45

Answer 1

The correct option is C 40

Number of guests that Pentagonal table can accomodate $=5$
($\because$ As there are 5 corners in pentagon)

Let the number of pentagonal table required be "n".
So, Number of guests that Pentagonal table "n" can accomodate$=5\times n=5n$

Number of guests that 1 square table can accomodate $=4\times 1=4$

Total number of guests = 204

Since there will be no empty seat,
Total number of guests = Number of guests that "n" pentagonal table can accomodate + Number of guests that 1 square table can accomodate = 204

$\Rightarrow 5\times n+4=204$

Subtract 4 from both the sides
$\Rightarrow 5\times n+4-4=204-4$
$\Rightarrow 5\times n=200$

Divide both side by 5.
$\Rightarrow \frac{5n}{5}=\frac{200}{5}$
$\Rightarrow n=40$

Hence, the number of pentagonal tables is 40.