If the length of a rectangle is increased by 10% and its breadth is decreased by 10%, then the area will change by what percentage of the original area?

1. A

   1% increase

2. B

   1% decrease

3. C

   No change

4. D

   5% decrease

Appeared in: AIIMS Delhi NO - 2018

Explanation

• When the length (L) is increased by 10%, the new length becomes 1.1L.
• When the breadth (B) is decreased by 10%, the new breadth becomes 0.9B.
• The new area is (1.1L) × (0.9B) = 0.99 × (L × B).
• Since the new area is 0.99 times the original area, it represents 99% of the original area.
• The reduction from 100% to 99% is a 1% decrease.

Why Other Options Were Wrong

• Option A: This is incorrect. A common mistake is to misinterpret the final result. The product of the multipliers (1.1 × 0.9) is 0.99, which is less than 1, indicating a decrease, not an increase.
• Option C: This is a very common misconception. A 10% increase and a 10% decrease do not cancel each other out when dealing with multiplication (area). The 10% decrease is applied to a larger value (the new length), resulting in a net change.
• Option D: This value is a result of incorrect calculation. The precise calculation using either the example method or the successive change formula yields a 1% decrease.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating percentage change in the area of a rectangle after successive changes in its dimensions as background academic context rather than a clinical decision trigger.
• This question tests fundamental mathematical aptitude, a skill essential for various non-clinical aspects of professional roles, including resource management, data interpretation, and administrative tasks.
• While not directly clinical, accurate calculation is a core competency that underlies many nursing tasks, such as medication dosage calculation, fluid balance monitoring, and interpreting percentage-based lab results.
• What if the length and breadth were both decreased by 10%? The new area would be (0.9L) × (0.9B) = 0.81LB, which is a 19% decrease.

How to Approach the Question

• Identify the core task: Find the net percentage change in the area of a rectangle.
• Recognize that area is a product (Length × Breadth), so percentage changes are multiplicative.
• Avoid the common trap of assuming that a 10% increase and a 10% decrease will cancel each other out to result in no change.
• Choose a reliable method for calculation. The simplest is often to assume initial dimensions of 10 or 100.
• Alternatively, use the formula for successive percentage change: Net % Change = x + y + (xy/100), where an increase is positive and a decrease is negative.
• Calculate the new area and compare it to the original area to determine the percentage change, paying attention to whether it's an increase or decrease.

Concept Tested & Keywords

• Concept Tested: Calculating percentage change in the area of a rectangle after successive changes in its dimensions.
• Stem keywords: rectangle, length, breadth, area, increased by 10%, decreased by 10%
• Lead-in keywords: change by what percentage
• Negative lead-in flag: false

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