The area of a rectangle gets increased by 30 square units, if its length is reduced by 3 units and breadth is increased by 5 units. If we increase the length by 5 units and reduce the breadth by 3 units then the area of a rectangle reduces by 10 square units. Find the length and breadth of the rectangle.

Let the length be x units and breadth be y units of a rectangle.

⇒ Area of rectangle = x × y

According to the question,

If length is reduced by 3, length = (x – 3)

And breadth is increased by 5, breadth = (y + 5)

Area = (xy + 30)

⇒ (x – 3)(y + 5) = (xy + 30)

⇒ xy + 5x – 3y – 15 = xy + 30

⇒ 5x – 3y = 45 …(i)

If length is incresed by 5, length = (x + 5)

And breadth is reduced by 3, breadth = (y – 3)

Area = (xy – 10)

⇒ (x + 5)(y – 3) = (xy – 10)

⇒ xy – 3x + 5y – 15 = xy – 10

⇒ – 3x + 5y = 5 …(ii)

Multiply (i) by 3 and (ii) by 5,

15x – 9y = 135 .. (iii)

– 15x + 25y = 25 …(iv)

Add (iii) and (iv),

15x – 9y – 15x + 25y = 135 + 25

⇒ 16y = 160

⇒ y = 10

Putting this in (i),

5x – 3×10 = 45

⇒ 5x = 45 + 30

⇒ 5x = 75

⇒ x = 15

So, the length is 15 units and breadth is 10 units.