Question
Download Solution PDFThe breadth of a rectangular lawn is decreased by 8% and its length is increased by 15%. Find the percentage change in the lawn area.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The breadth of a rectangular lawn is decreased by 8% and its length is increased by 15%.
Formula used:
Percentage change in area = (New Length × New Breadth - Original Length × Original Breadth) / (Original Length × Original Breadth) × 100
Calculation:
Let the original length be L and the original breadth be B.
New Length = L + 0.15L = 1.15L
New Breadth = B - 0.08B = 0.92B
Original Area = L × B
New Area = 1.15L × 0.92B
Percentage change in area = ((1.15L × 0.92B) - (L × B)) / (L × B) × 100
⇒ Percentage change in area = ((1.058L × B) - (L × B)) / (L × B) × 100
⇒ Percentage change in area = (1.058 - 1) × 100
⇒ Percentage change in area = 0.058 × 100
⇒ Percentage change in area = 5.8%
∴ The correct answer is option (4).
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