The question is simple however it was added to show that the final answer is not affected by the ratio of length,breadth, height i.e for any ratio the volume will increase by 17 times only for the corresponding percentage increments.
Consider the length as x
b=2x and h=3x
Now length increased by 100% i.e new l =2x
Now breadth increased by 200% i.e new b =6x
Now height increased by 200% i.e new h =9x
New volume =2x*6x*9x=\(108x^3\)
Old volume = \(6x^3\)
New volume/old volume=\(108x^3/6x^3=18\)
New volume= 18*old volume
= (1+17) old volume
= old volume+ 17 old volume
Therefore the old volume increased by 17 times.
Now consider l=b=h=x
Now length increased by 100% i.e new l =2x
Now breadth increased by 200% i.e new b =3x
Now height increased by 200% i.e new h =3x
New volume = \(18x^3\)
old volume = \(x^3\)
New volume / old volume = 18
Old volume increased by 17 times.
Therefore the quicker way to solve the problem is simply by considering only the percentage or say the observation is that the ratio is just a distraction.
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