The length of a rectangle is increased by 10% and its breadth is decreased by 10%, then the area of the new r… - RRB Staff Nurse Mumbai-2015

RRB Staff Nurse Mumbai-2015

Non Nursing Subjects

Medium

Appeared in: RRB Staff Nurse Mumbai-2015

Explanation

When two successive percentage changes occur, the net effect is not simply their sum. Here, one dimension increases and the other decreases.
The new length becomes 1.1 times the original, and the new breadth becomes 0.9 times the original.
The new area is the product of the new dimensions: (1.1 × 0.9) = 0.99 times the original area.
A factor of 0.99 means the new area is 99% of the original, which is a 1% decrease from 100%.
A shortcut formula for successive percentage changes (x and y) is (x + y + xy/100)%. For this problem, (+10 - 10 + (10 × -10)/100)% = -1%.

Option A: This is a common misconception. A 10% increase and a 10% decrease do not cancel each other out because they are calculated on different base values (the original length and breadth).
Option B: This is the opposite of the correct answer. An increase would occur if both dimensions were increased, or if the decrease was smaller than the increase in a way that their product is greater than 1.
Option D: This incorrectly assumes that the 10% decrease in one dimension directly translates to a 10% decrease in the total area, ignoring the counteracting effect of the 10% increase in the other dimension.

Visual 1: Diagram - An infographic showing an original rectangle with dimensions L and B, and a new rectangle with dimensions 1.1L and 0.9B, visually comparing their areas to show the slight decrease.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Percentage change in area of a rectangle as background academic context rather than a clinical decision trigger.
This question tests quantitative aptitude, a non-nursing subject area often included in the general aptitude section of nursing recruitment examinations.
Strong numerical skills are essential for nurses for tasks like medication dosage calculation, interpreting lab results, and monitoring patient vitals, making quantitative reasoning a relevant skill to assess.
What if? - If both the length and breadth were decreased by 10%, the net change would be (-10 - 10 + (-10 × -10)/100)% = (-20 + 1)% = -19%. The area would decrease by 19%.

How to Approach the Question

Step 1: Identify the two percentage changes given in the problem. Note whether they are an increase (+) or a decrease (-). Here, we have +10% and -10%.
Step 2: Recall the formula for successive percentage changes: Net % Change = (x + y + (xy/100))%.
Step 3: Substitute the values into the formula: x = 10 and y = -10.
Step 4: Calculate the result: (10 - 10 + (10 × -10)/100) = (0 - 100/100) = -1.
Step 5: Interpret the sign of the result. A negative sign means a decrease, and a positive sign means an increase. Here, -1 means a 1% decrease.
Step 6: Select the option that matches your calculated result.

Concept Tested & Keywords

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

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