The length of a rectangular plot is increased by 20 percent by how much percentage its breadth should be decreased so that total area remains same?

1. A

   20 percent

2. B

   16.66 percent

3. C

   25 percent

4. D

   15 percent

Appeared in: CIP Ranchi 2023

Explanation

• To keep the area of a rectangle (Area = Length × Breadth) constant, if the length increases, the breadth must decrease proportionally.
• Let the new length be L' = 1.20 × L (a 20% increase).
• For the area to remain the same, L × B = L' × B' → L × B = (1.20 L) × B'.
• Solving for the new breadth (B'), we get B' = B / 1.20 = (5/6) × B.
• The decrease in breadth is B - (5/6)B = (1/6)B.
• The percentage decrease is (1/6) × 100, which equals 16.66%.

Why Other Options Were Wrong

• Option A: A 20% increase followed by a 20% decrease results in a net decrease of 4% in the total area, not a constant area. The changes are not symmetrical.
• Option C: A 25% decrease in breadth would overcompensate for the 20% increase in length, resulting in a smaller total area (1.20 L × 0.75 B = 0.90 LB).
• Option D: This is a calculation error. A 15% decrease in breadth is insufficient to offset the 20% increase in length, leading to a larger total area (1.20 L × 0.85 B = 1.02 LB).

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the understanding of percentage changes and their application in maintaining a constant product, specifically the area of a rectangle as background academic context rather than a clinical decision trigger.
• This type of calculation is analogous to medication dosage adjustments. If the concentration of a drug solution is increased, the volume administered must be decreased to deliver the same total dose.
• It is also relevant in fluid management. If the rate of an IV infusion is increased, the time required to infuse a specific volume of fluid will decrease.
• What if the length was decreased by 20%? To keep the area the same, the breadth would need to be increased. The new length would be 0.80 L. The new breadth would need to be B / 0.80 = 1.25 B, which is a 25% increase.

How to Approach the Question

• First, identify the relationship between the variables: Area = Length × Breadth.
• Recognize that the final area must equal the initial area.
• Express the change in the first variable mathematically. An increase of 20% means the new value is 100% + 20% = 120% or 1.2 times the original.
• Set up the equation: (Original Length × Original Breadth) = (New Length × New Breadth).
• Substitute the known values: (L × B) = (1.2 L × New Breadth).
• Solve for the 'New Breadth' in terms of the 'Original Breadth'. You will find New Breadth = B / 1.2.

Concept Tested & Keywords

• Concept Tested: This question tests the understanding of percentage changes and their application in maintaining a constant product, specifically the area of a rectangle.
• Stem keywords: rectangular plot, length, breadth, increased by 20 percent, decreased, area remains same
• Lead-in keywords: by how much percentage

Question ID

QEtogwKth71fTYnwcqT2IS

Copy ID