The length of a rectangle is increased by 10% and its breadth is decreased by 10%, then, the area of the new rectangle is

Appeared in: RRB Staff Nurse Ahmedabad-2015

Explanation

When a value is increased by x% and then decreased by x%, the final result is always a net decrease.
Let the original length be L and breadth be B. The original area is A = L × B.
The new length is L' = L × (1 + 10/100) = 1.1L.
The new breadth is B' = B × (1 - 10/100) = 0.9B.
The new area is A' = L' × B' = (1.1L) × (0.9B) = 0.99 × (L × B) = 0.99A.
The change is 1 - 0.99 = 0.01, which corresponds to a 1% decrease.

Option A: This is a common misconception. The percentage increase and decrease are applied to different base values (the original length and breadth), so their effects do not cancel out perfectly.
Option B: The calculation results in a product of 1.1 and 0.9, which is 0.99, indicating a decrease, not an increase.
Option D: A 10% decrease would result in a new area of 0.90 times the original. The calculated new area is 0.99 times the original.

Visual 1: Infographic: A diagram showing an original 10x10 square (Area=100) transforming into a new 11x9 rectangle (Area=99) to visually represent the 1% decrease.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Successive Percentage Change as background academic context rather than a clinical decision trigger.
This question tests general mathematical aptitude and problem-solving skills, which are essential for non-nursing sections of competitive examinations.
While not a direct clinical skill, the ability to perform quick percentage calculations is useful in various settings, such as understanding changes in lab values or calculating medication dosage adjustments.
What if? If the length was increased by 20% and breadth decreased by 20%, the new area would be 1.2 × 0.8 = 0.96 of the original, representing a 4% decrease (not a 2% decrease).

How to Approach the Question

Identify that this is a successive percentage change problem.
Assign simple initial values for length and breadth, like 10 and 10, to make calculation easier. Calculate the original area (10x10=100).
Calculate the new length after a 10% increase (10 + 1 = 11).
Calculate the new breadth after a 10% decrease (10 - 1 = 9).
Calculate the new area by multiplying the new dimensions (11x9=99).
Determine the percentage change from the original area (100) to the new area (99), which is a 1% decrease.

Concept Tested & Keywords

Concept Tested: Successive Percentage Change
Stem keywords: rectangle, length, breadth, area, increased by 10%, decreased by 10%
Lead-in keywords: the area of the new rectangle is

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