Question : The length and breadth of a cuboid are increased by 20% and 25%, respectively, while its height is reduced by 30%. What must be the total percentage increase/decrease in the volume of the cuboid?
Option 1: Increase by 5%
Option 2: Increase by 3%
Option 3: Decrease by 2%
Option 4: Decrease by 4%
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Correct Answer: Increase by 5%
Solution :
Given: The length and breadth of a cuboid are increased by 20% and 25% and height is reduced by 30%.
Let initial length be $l$, breadth be $b$ and height be $h$.
Initial volume = $lbh$
After the length and breadth of a cuboid are increased by 20% and 25% and height is reduced by 30%,
Final length = $1.2l$
Final breadth = $1.25b$
Final height = $0.7h$
Final volume = $1.2l×1.25b×0.7h$ = $1.05lbh$
Increase in volume = $\frac{1.05lbh-lbh}{lbh}×100$ = 5%
Hence, the correct answer is 'increase by 5%'.
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