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NTPC Graduate Tier 1 2025 Shift-2 📅 06 Jun, 2025

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)?

A
575
B
576
C
573
D
574
Result Summary
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NTPC Graduate Tier 1
2025 • 06 Jun, 2025 • Shift-2
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)?
Correct Answer
574
Formulating Equations: Let the original length be L and breadth be B. The first condition gives (L + 5)(B - 7) = LB + 8, which expands and simplifies nicely to ......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Mensuration
Pg. No -
💡 Analysis & Explanation
Formulating Equations ▼
Let the original length be L and breadth be B. The first condition gives (L + 5)(B - 7) = LB + 8, which expands and simplifies nicely to -7L + 5B = 43.
Second Condition Setup ▼
The second scenario gives (L - 5)(B + 8) = LB + 33, which expands and simplifies directly to 8L - 5B = 73.
Solving for Dimensions ▼
Adding both linear equations naturally eliminates B: (-7L + 8L) + (5B - 5B) = 43 + 73, yielding L = 116. Substituting L = 116 into the first equation gives 5B = 43 + 7(116) = 855, definitively making B = 171.
Calculating Perimeter ▼
The total perimeter of a rectangle is mathematically expressed as 2(L + B). Thus, calculating 2(116 + 171) = 2 × 287 gives 574 meters.
Conclusion ▼
The original perimeter is 574 m.
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