# 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)

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)

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)

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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Pair of Linear Equations in Two Variables46 mins
Bonus on Applications of Linear Equations in Two Variables43 mins
Dealing With the Real Life Problems53 mins
HOT Topics of Applications of Linear Equations in Two Variables52 mins
NCERT I Quiz on Solution of Linear Equations in Two Variables49 mins
Learn to Solve Real Life Problems Using Linear Equations in Two Variables36 mins
Quiz | Solution of Linear Equations53 mins
Champ Quiz | Consistency and Inconsistency of Solutions36 mins
Smart Revision | Important Word Problems37 mins
Quiz | Real Life Problems Through Linear Equations56 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses