John has a cuboidal box whose length. breadth and height are in the ratio 2 : 3 : 5. If the length, the breadth and the height of this box are each increased by100% to make a new box. then the volume of the new box is how many times the volume of the old box?

Correct option is A

Given:

Dimension of cuboid are in ratio 2:3:5

All length , breadth and height are increased by 100%

Formula Used:

Volume of cuboid = $$l\times b \times h$$​​

Solution:

Let the dimension of cuboid be 2x, 3x and 5x

Then volume = (2x)(3x)(5x) = 30$$x^3$$​​

New length = 2x + 100% of 2x = 4x

Breadth = 3x + 3x = 6x

Height = 5x + 5x = 10x

New volume = (4x)(6x)(10x) = 240$$x^3$$​​

Ratio of new volume to old volume =$$\frac{240x^3}{30x^3}$$ = 8

Hence, new volume is 8 times the old volume