The length of a rectangle is twice its breadth. If its lengthis decreased by 5cm & breadth is increased by 5cm, the area of the rectangle is increased by 75sq.cm. What is the length of the rectangle?
Answers
A) 25 cm	B) 30 cm	C) 40 cm	D) 45 cm	E) 60 cm

Rationale: let breadth = x cm then , length = 2 x cm area = x × 2 x = 2 x 2 sq . cm . new length = ( 2 x − 5 ) cm new breadth = ( x + 5 ) cm new area = ( 2 x − 5 ) ( x + 5 ) sq . cm . given that , new area = initial area + 75 sq . cm . ⇒ ( 2 x − 5 ) ( x + 5 ) = 2 x 2 + 75 ⇒ 2 x 2 + 10 x − 5 x − 25 = 2 x 2 + 75 ⇒ 5 x − 25 = 75 ⇒ 5 x = 75 + 25 = 100 ⇒ x = 1005 = 20 cm length = 2 x = 2 × 20 = 40 cm c
Answer: C