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 and the breadth is increased by 5 m. The area of the floor is :
1. 280 m2
2. 250 m2
3. 300 m2
4. 325 m2
1. 280 m2
2. 250 m2
3. 300 m2
4. 325 m2
Correct Answer – Option 3 : 300 m2
Given:
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 and the breadth is increased by 5 m
Concept used:
Area of Rectangle = Length × Breadth
Calculation:
Let the breadth of the floor be x m.
Length = (x + 20) meter
The area of the floor = Length × Breadth
Area of the floor = (x + 20) x m2
According to the question
Length is decreased by 10 m = (x + 20 – 10) = (x + 10) m
Breadth is increased by 5 m = (x + 5) m
⇒ (x + 10) (x + 5) = x (x + 20)
⇒ x2 + 15x + 50 = x2 + 20x
⇒ 5x = 50
⇒ x = 10 meter
Length of the floor = x + 20 = 30 m
Area of the floor = 30 × 10
∴ Area of the floor = 300 m2