Question

There are 500 seats in minerva cinema, mumbai, placed in similar rows. After the reconstruction of the hall, the total number of seats became 10% less. The number of rows was reduced by 5 but each row contained 5 seats more than before. How many rows and how many seats in a row were there initially in the hall?

Answer 1

Answer: Total number of rows = 20

Total number of seats in a row = 25

Step-by-step explanation:

Let x represents total number of rows and y represents total seats in a row,

Then, According to the question,

x y = 500 ------- (1)

Also, the total number of seats became 10% less when the number of rows was reduced by 5 and number of seats in a row is increased by 5.

That is, (x-5)(y+5) = (100-10)% of 500

⇒ xy - 5y + 5x - 25 = 90% of 500

⇒ xy - 5y + 5x - 25 = 450

⇒ xy - 5y + 5x = 475

From equation (1),

We get, 500 - 5y + 5 × 500/y = 475

⇒ -5y + 2500/y = 475 - 500

⇒-5y + 2500/y = -25

⇒ y - 500/y = 5

⇒ $y^2 - 5y - 500 = 0$

⇒ y = - 20 or 25

But Number of seats can not be negative,

Thus, y = 25

By putting this value in equation (1) we get,

x = 20

Thus, Initially, the total number of rows(x) = 20 and the total number of seats in a row(y) = 25