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Question
In an auditorium, the number of rows are equal to the number of seats in each row.If the number of rows is doubled and number of seats in each row is reduced by 5, then the total number of seats is increased by 375. How many rows were there?
Solution
Let the number of rows = x
then no. of seats in each row = x
and total number of seats = x × x = x2
According to the condition,
2x x (x - 5) = x2 + 375
⇒ 2x2 - 10x = x2 + 375
⇒ 2x2 - 10x - x2 - 375 = 0
⇒ x2 - 10x - 375 = 0
⇒ x2 - 25x + 15x - 375 = 0
⇒ x(x - 25) + 15(x - 25) = 0
⇒ (x - 25)(x + 15) = 0
Either x - 25 = 0,
then x = 25
or
x + 15 = 0,
then x = -15,
but it is not possible as it is negative.
∴ Number of rows = 25.
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