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Question
The number of seats in a row is equal to the total number of rows in a hall. The total number of seats in the hall will increase by 375 if the number of rows is doubled and the number of seats in each row is reduced by 5. Find the number of rows in the hall at the beginning.
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Solution
Let the number of rows in the hall be “x”
∴ Total number of rows = x
Total number of seats in the hall is “x2”
By the given condition
x2 + 375 = 2x (x – 5)
x2 + 375 = 2x2 – 10x
x2 – 2x2 + 10x + 375 = 0
– x2 + 10x + 375 = 0
– x2 – 10x – 375 = 0
(x – 25) (x + 15)
x – 25 = 0 or x + 15 = 0
x = 25 or x = – 15
Number of rows in the hall = 25
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