The length, breadth and height of a cuboid are in the ratio 1:2:3. The length, breadth and height of the cuboid are increased by 200%,300% and 300%, respectively. Then compared to the original volume, the increase in the volume of the cuboid will be:

​Given:

The original dimensions (length, breadth, height) of the cuboid are in the ratio 1:2:3.

The length is increased by 200%, the breadth by 300%, and the height by 300%

Volume of a Cuboid:  The volume V of a cuboid is given by:

V = $$\text{Length} \times \text{Breadth} \times \text{Height}$$

Solution: ​

Original volume = 10$$\times$$ 20$$\times$$ 30 = 6000 $$unit^3$$ 

Now, 

New volume = 30$$\times$$80$$\times$$120 = 288000 $$unit^3$$ 

Increase in volume = 288000 - 6000 = 282000$$unit^3$$ 

Times Increase in volume = $$\frac{282000}{6000} = 47$$​ 

Therefore, the new volume has a 47 times increment in original volume.