Question 54

Logical Reasoning Percentage Easy

The percentage change in area of a rectangle by decreasing its length and increasing its breadth by 5% is

(A) 0.25% decrease
(B) no change
(C) 0.25% increase
(D) 2.5% increase
✓ Correct Answer: Option A Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

\[ \text{Let the original length be } L \text{ and breadth be } B. \] \[ \text{Original area: } A = L \times B \] \[ \text{New length (decreased by 5\%): } 0.95L, \quad \text{New breadth (increased by 5\%): } 1.05B \] \[ \text{New area: } A' = (0.95L)(1.05B) = 0.9975 \, (LB) \] \[ \text{Percentage change in area} = \frac{A' - A}{A} \times 100 = (0.9975 - 1) \times 100 = -0.25\% \] \[ \boxed{\text{The area decreases by } 0.25\%} \]

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