Banner 0
Banner 1
Banner 2
Banner 3
Banner 4
Banner 5
Banner 6
Book Online Demo
Check Your IQ
Try Test

Courses

Dropper NEET CourseDropper JEE CourseClass - 12 NEET CourseClass - 12 JEE CourseClass - 11 NEET CourseClass - 11 JEE CourseClass - 10 Foundation NEET CourseClass - 10 Foundation JEE CourseClass - 10 CBSE CourseClass - 9 Foundation NEET CourseClass - 9 Foundation JEE CourseClass -9 CBSE CourseClass - 8 CBSE CourseClass - 7 CBSE CourseClass - 6 CBSE Course
Offline Centres

Q.

The area of a rectangle gets reduced by 80 sq units, if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, then the area is increased by 50 sq units. Find the length and the breadth of the rectangle by the elimination method.


see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away
An Intiative by Sri Chaitanya

a

Length =70 units, Breadth =40units

b

Length =20 units, Breadth =10units

c

Length =50 units, Breadth =80units

d

Length =40 units, Breadth =30units 

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given that the area of rectangle reduced by 80 sq. units, when length reduced by 5 units and breadth increased by 2 units and area of rectangle increased by 50 sq. units, when length increased by 10 units and breadth decreased by 5 units
Consider x and y to be the length and the breadth of the rectangle.
Then, the area of a rectangle = xy
According to the given condition,  (x−5)(y+2)=xy−80 ⇒2x−5y=−70…(i) (x+10)(y−5)=xy+50 ⇒−5x+10y=100…(ii)  
Multiplying Eq. (i) by 5 and Eq. (ii) by 2 , we get  10x−25y=−350…(iii) −10x+20y=200…(iv)  
Adding equations (iii) and (iv), we get  −5y=−150 ⇒y=30  
Substituting the value of y in Eq. (ii), we get  2x−5×30=−70 ⇒x=40  
Therefore, the length =40 units and breadth =30 units.
Hence, option (4) is correct.
 
Watch 3-min video & get full concept clarity
Related Blogs
Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation
Result Producing online coaching for JEE/NEET of south India
Largest All India Test Series for JEE/NEET
Best Books for IIT JEE
Best Books for NEET
How to Join IIT after 10th

Best Courses for You

JEE

JEE

NEET

NEET

Foundation JEE

Foundation JEE

Foundation NEET

Foundation NEET

CBSE

CBSE

score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

Related Blogs
Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation
Result Producing online coaching for JEE/NEET of south India
Largest All India Test Series for JEE/NEET
Best Books for IIT JEE
Best Books for NEET
How to Join IIT after 10th
whats app icon