Question : If both the length and breadth of a cuboid are increased by 12 percent, then by how much percent its height should be reduced so that the volume of the cuboid remains the same?
Option 1: 14.56 percent
Option 2: 24.72 percent
Option 3: 20.28 percent
Option 4: 28.44 percent
Correct Answer: 20.28 percent
Solution :
Let the length be 100, breadth be 100 and height be 100.
The volume of a cuboid = Length × Breadth × Height
So, volume = 100 × 100 × 100 = 1000000
Now, the length and breadth of a cuboid are increased by 12 percent.
Let the new height be $h$.
According to the question,
1000000 = 112 × 112 × $h$
⇒ $h$ = 79.72
So, the height has been reduced $=100-79.72=20.28$
Hence, the correct answer is 20.28 percent.
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