The length of a room floor exceeds its breadth by 20 m. The area of the floor remains unaltered when the length is decreased by 10 m but the breadth is increased by 5 m. The area of the floor (in square metres) is :(1) 280 (2) 325(3) 300 (4) 420

Solution

Let the breadth of floor be x metre.

:. Length = (x + 20) metre

:. Area of the floor

=(x+ 20) x sq. metre

According to question.

(x + 10) (x + 5) = x (x + 20)

⇒x² + 15x + 50 = x² + 20x

⇒ 20x = 15x + 50

⇒ 5x= 50

⇒ x = 10 metre

:. Length = x+ 20 = 10 + 20

= 30 metre

:. Area of the floor = 30 x 10

= 300 sq. metre