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%
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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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