Question : If both the length and breadth of a cuboid are increased by 50%, then by how much percentage its height should be reduced so that its volume remains the same?
Option 1: 62.34%
Option 2: 55.56%
Option 3: 37.25%
Option 4: 48.75%
Correct Answer: 55.56%
Solution :
Let the length, height and breadth be 100 each.
We know the volume of a cuboid = Length × Breadth × Height = 100 × 100 × 100 = 1000000
Both the length and breadth of a cuboid are increased by 50%.
New length = New breadth = 100 + 50 = 150
$\therefore$ New height = $\frac{1000000}{150×150}=44.44$
So, required percentage $=\frac{100-44.44}{100}×100=55.56\%$
Hence, the correct answer is 55.56%.
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