Question

Three nos. are in the ratio of 2:3:4 . The sum of their cube is 0.334125 . Find the nos.

Answer 1

Let the numbers be 2x,3x,4x

8x^3 + 27x^3 +64x^3 = 0.334125

99x^3 = 0.334125

x= 0.15

So, the numbers are 0.3,0.45, 0.6

Answer 2

The ratio of three numbers is 2:3:4.
Let the numbers be 2x, 3x and 4x.
Cubes of numbers = (2x)3, (3x)3, (4x)3 = 8x3, 27x3, 64x3
8x3 + 27x3 + 64x3 = 99x3
99 x3 = 0.334125
x3 = (0.334125) / 99
x3 = 0.003375
x3 = (0.15)3
x = 0.15
Therefore, the numbers are (2 x 0.15), (3 x 0.15) and (4 x 0.15) i.e. 0.3, 0.45 and 0.6

There's an alternate method too:

(2x)³ + (3x)³ + (4x)³ = 0.334125 

⇒ 8x³ + 27x³ + 64x³ = 0.334125 

⇒ 99x³ = 0.334125 

  ⇒ x = 0.15 

So, The three numbers are: 

 ∴    2(0.15) = 0.3 ,   
       3(0.15) = 0.45,   
and, 4(0.15) = 0.6

Hope This Helps :)