The area of a rectangle increases by 8 m2 if its length is increased by 5 m and breadth is decreased by 7 m. If the length is decreased by 5 m and breadth is increased by 8 m,  then its area increases by 33 m2. What is the perimeter of the original rectangle (in m)?

This question was previously asked in
RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 2)
View all RRB NTPC Papers >
  1. 575
  2. 573
  3. 574
  4. 576

Answer (Detailed Solution Below)

Option 3 : 574
Free
RRB NTPC Graduate Level Full Test - 01
2.4 Lakh Users
100 Questions 100 Marks 90 Mins

Detailed Solution

Download Solution PDF

Given:

Scenario 1: Length increased by 5 m, Breadth decreased by 7 m, Area increases by 8 m2.

Scenario 2: Length decreased by 5 m, Breadth increased by 8 m, Area increases by 33 m2.

Formula used:

Area of rectangle = Length × Breadth (l × b)

Perimeter of rectangle = 2 × (Length + Breadth)

Calculations:

Let the original length of the rectangle be 'l' meters and the original breadth be 'b' meters.

Original Area = l × b

From Scenario 1:

New length = (l + 5) m

New breadth = (b - 7) m

New Area = (l + 5)(b - 7)

Given that the area increases by 8 m2:

(l + 5)(b - 7) = lb + 8

⇒ lb - 7l + 5b - 35 = lb + 8

⇒ -7l + 5b = 8 + 35

⇒ -7l + 5b = 43 (Equation 1)

From Scenario 2:

New length = (l - 5) m

New breadth = (b + 8) m

New Area = (l - 5)(b + 8)

Given that the area increases by 33 m2:

(l - 5)(b + 8) = lb + 33

⇒ lb + 8l - 5b - 40 = lb + 33

⇒ 8l - 5b = 33 + 40

⇒ 8l - 5b = 73 (Equation 2)

Now, we have a system of two linear equations:

1) -7l + 5b = 43

2) 8l - 5b = 73

Add Equation 1 and Equation 2:

(-7l + 5b) + (8l - 5b) = 43 + 73

⇒ -7l + 8l + 5b - 5b = 116

⇒ l = 116

Substitute the value of l into Equation 1:

-7(116) + 5b = 43

⇒ -812 + 5b = 43

⇒ 5b = 43 + 812

⇒ 5b = 855

⇒ b = 171

So, the original length (l) = 116 m and original breadth (b) = 171 m.

Perimeter of the original rectangle = 2 × (l + b)

⇒ Perimeter = 2 × (116 + 171)

⇒ Perimeter = 2 × 287

⇒ Perimeter = 574 m

∴ The perimeter of the original rectangle is 574 m.

Latest RRB NTPC Updates

Last updated on Jul 17, 2025

-> RRB NTPC Under Graduate Exam Date 2025 has been released on the official website of the Railway Recruitment Board.

-> The RRB NTPC Admit Card will be released on its official website for RRB NTPC Under Graduate Exam 2025.

-> UGC NET Result 2025 out @ugcnet.nta.ac.in

-> HSSC CET Admit Card 2025 has been released @hssc.gov.in

-> Candidates who will appear for the RRB NTPC Exam can check their RRB NTPC Time Table 2025 from here. 

-> The RRB NTPC 2025 Notification released for a total of 11558 vacancies. A total of 3445 Vacancies have been announced for Undergraduate posts like Commercial Cum Ticket Clerk, Accounts Clerk Cum Typist, Junior Clerk cum Typist & Trains Clerk.

-> A total of 8114 vacancies are announced for Graduate-level posts in the Non-Technical Popular Categories (NTPC) such as Junior Clerk cum Typist, Accounts Clerk cum Typist, Station Master, etc.

-> Prepare for the exam using RRB NTPC Previous Year Papers.

-> Get detailed subject-wise UGC NET Exam Analysis 2025 and UGC NET Question Paper 2025 for shift 1 (25 June) here

->Bihar Police Driver Vacancy 2025 has been released @csbc.bihar.gov.in.

More Plane Figures Questions

More Mensuration Questions

Get Free Access Now
Hot Links: teen patti all game teen patti casino apk teen patti jodi teen patti all app