The breadth of a rectangular lawn is decreased by 8% and its length is increased by 15%. Find the percentage change in the lawn area.

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SSC CPO 2024 Official Paper-I (Held On: 29 Jun, 2024 Shift 2)
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  1. 8.5% decrease
  2. 8.5% increase
  3. 5.8%decrease
  4. 5.8% increase

Answer (Detailed Solution Below)

Option 4 : 5.8% increase
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Detailed Solution

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Given:

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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