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There are 500 seats in a classroom placed in a similar row. After the reconstruction of the classroom, 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 classroom?

There are 500 seats in a classroom placed in a similar row. After the reconstruction of the classroom, 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 classroom? Correct Answer 20 rows 25 seats

Let there are x rows and number of seats in each row is y

So, according to the question,

⇒ xy = 500

Also, after the reconstruction of classroom,

The seats became 10% less than before

⇒ 500 – 10% of 500 = 500 – 50 = 450

⇒ (x – 5) (y + 5) = 450

⇒ xy + 5x – 5y – 25= 450

Putting the value of xy, we get,

⇒ 500 + 5x – 5y = 475

⇒ y – x = 5

⇒ y = x + 5

So,

⇒ x (x + 5) = 500

⇒ x2 + 5x – 500 = 0

⇒ x2 + 25x – 20x – 500 = 0

⇒ (x + 25) (x – 20) = 0

⇒ x = 20, -25

Since, -25 is not possible

⇒ x = 20

⇒ y = 25

∴ Number of rows are 20 and number of columns are 25

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