Question

In a movie theatre seating 625 people, the number of rows in front of Sheila is thrice the number of rows behind her. Also, the number of seats to her left is twice the number of seats to her right. Find where Sheila is sitting.

(There are as many seats in a row as there are rows in total. Count the rows from the front to the back and the seats from the left to the right with respect to Sheila.)

• A. 18th seat in the 16th row
• B. 19th seat in the 17th row
• C. 17th seat in the 19th row
• D. 16th seat in the 18th row

Answer 1

The correct option is C 17th seat in the 19th row

$Totalcapacityofthetheatre=625=25\times 25$

Also, if
$Numberofseatsineachrow=NTotalnumberofrows=R$
$⟹N=R$
$⟹N=R=25$

Now,
$NumberofrowsbehindSheila=x$
$⟹NumberofrowsaheadofSheila=3x$

So, total number of rows, including Sheila's seat, we get:
$x+3x+1=25$
$⟹4x=24$
$⟹x=6$
$⟹3x=18$

Hence, Sheila is sitting in the (3x+1)th row from the front or the 19th row from the front.

Similarly,
$NumberofseatstoSheil{a}^{\prime }sright=y$
$⟹NumberofseattoSheil{a}^{\prime }sleft=2y$

So, total number of seats in that row, including Sheila's seat, we get:
$y+2y+1=25$
$⟹3y=24$
$⟹y=8$
$⟹2y=16$

Hence, Sheila is sitting on the (2y + 1)th seat from her left or the 17th seat from her left.

Therefore, Sheila's position in the theatre is the 17th seat in the 19th row.