The total percentage change in the volume of a cuboid if its length and breadth are decreased by 15% and 25%, respectively, while its height is increased by 60% is:

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SSC CPO 2024 Official Paper-I (Held On: 29 Jun, 2024 Shift 2)
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  1. 5% decrease
  2. 2% decrease
  3. 2% increase
  4. 5% increase

Answer (Detailed Solution Below)

Option 3 : 2% increase
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Detailed Solution

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Given:

The total percentage change in the volume of a cuboid if its length and breadth are decreased by 15% and 25%, respectively, while its height is increased by 60%.

Formula used:

Volume change percentage = (1 + ΔL) × (1 + ΔB) × (1 + ΔH) - 1

Where:

ΔL = percentage change in length

ΔB = percentage change in breadth

ΔH = percentage change in height

Calculation:

ΔL = -15% = -0.15

ΔB = -25% = -0.25

ΔH = 60% = 0.60

Volume change percentage = (1 - 0.15) × (1 - 0.25) × (1 + 0.60) - 1

⇒ Volume change percentage = 0.85 × 0.75 × 1.60 - 1

⇒ Volume change percentage = 1.02 - 1

⇒ Volume change percentage = 0.02

⇒ Volume change percentage = 2%

∴ The correct answer is option (3).

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