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If the length of rectangle is decreased by 25% and its breadth is increased by 30% then by how much percent its area is increased or decreased?
- A2.5% increased
- B2.5% decreased
- C5% increased
- D5% decreased
Answer not set
Discussion 1
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CCommunity
Area of rectangle = length × breadth
Let Length of rectangle be a and breadth be b
∴ Original area = a × b = ab
New area = (a – 25% of a) × (b + 30% of b)
⇒ New area = 0.75a × 1.3b
⇒ New area = 0.975ab
? 0.975ab < ab, area has decreased
Percent decrease in area = (Original area - New area) × 100/ Original area
⇒ Percent decrease = (ab - 0.975ab) × 100/ab
⇒ Percent decrease = 0.025 × 100 = 2.5%.
Let Length of rectangle be a and breadth be b
∴ Original area = a × b = ab
New area = (a – 25% of a) × (b + 30% of b)
⇒ New area = 0.75a × 1.3b
⇒ New area = 0.975ab
? 0.975ab < ab, area has decreased
Percent decrease in area = (Original area - New area) × 100/ Original area
⇒ Percent decrease = (ab - 0.975ab) × 100/ab
⇒ Percent decrease = 0.025 × 100 = 2.5%.