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The length and breadth of a cuboid is increased by 25% and 50% respectively while height is decreased by 20% and the side of a cube is decreased by 33.33%, then find the ratio of new volume of cuboid to the new volume of cube where the ratio of length, breadth, height of cuboid and side of cube is 2 : 1 : 1 : 3.

The length and breadth of a cuboid is increased by 25% and 50% respectively while height is decreased by 20% and the side of a cube is decreased by 33.33%, then find the ratio of new volume of cuboid to the new volume of cube where the ratio of length, breadth, height of cuboid and side of cube is 2 : 1 : 1 : 3. Correct Answer 3 : 8

Formula used:

Volume of cube = a3

Volume of cuboid = l × b × h

Calculation:

Let the ratio be x

So, length of cuboid = 2x

Breadth of cuboid = x

Height of cuboid = x

Side of cube = 3x

After increment and decrement in the length

Length of cuboid = 2x × 125% = 5x/2

Breadth of cuboid = x × 150% = 3x/2

Height of cuboid = x × 80% = 4x/5

And the side of cube = 3x × 66.66% = 2x

Now,

New volume of cuboid = 5x/2 × 3x/2 × 4x/5 = 3x3

New volume of cube = (2x)3 = 8x3

So, the required ratio = 3x3 : 8x3

Hence, 3 : 8

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