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The length, breadth and height of cuboid are in the ratio 1:2:3. If they are increased by 100%, 200% and 200% respectively, then, as compared to the original volume the increase in the volume of the cuboid will be:
A. 5 times
B. 18 times
C. 12 times
D. 17 times

Answer
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Hint: Take the proportionate as ‘x’. thus get the length, breadth and height of the original cuboid. Then find l,b & h, new, increased side. Then find the volume of the original cuboid and new increased volume of the cuboid. Subtract them to find the increases in volume of cuboid.

Complete step-by-step answer:
We have been given a cuboid whose length, breadth and height in the ratio 1:2:3. Now let us take ‘x’ as the side.
The length of cuboid =1.x=x .
The breadth of cuboid =2.x=2x .
The height of cuboid =3.x=3x .
Now their dimensions of the cuboid are increased by 100%, 200% and 200%. i.e. the length of cuboid is increased by 100%, the breadth is increased by 200% and the height is increased by 200%.
Hence, the new dimensions of the cuboid are
Length =x+100100x=x+x=2x .
Breadth =2x+200100×2x=2x+4x=6x .
Height =3x+200100×3x=3x+6x=9x .
Hence, the original dimensions of cuboid =x,2x,3x .
New dimensions of the cuboid =2x,6x,9x .
We know that volume of a cuboid =length×breadth×height .
Original volume of cuboid =x×2x×3x=6x3
Now increased volume of cuboid =2x×6x×9x=108x3
Thus the increase in volume = New increased volume – original volume of cuboid
=108x36x3=102x3
Thus we can write the increase in volume as,
102x3=17×6x3
We know that 6x3 is the original value.
Increase in volume =17× Original volume
Thus, when comparing the original volume the increase in the volume of cuboid is 17 times.
Option (D) is the correct answer.

Note: It is said length, breadth and height are in ratio. Don’t take different variables for the 3 quantities as l,b,h etc. take as they are in proportionate as ‘x’. putting 3 variables is complicated and you won't get the answer.
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