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

Given:

Let the three numbers are 2x, 3x and 4x

Acc. To given condition:

i.e (2x)³ + (3x)³ + (4x)³ = 0.334125

⇒ 8(x)³ + 27(x)³ + 64(x)³ = 0.334125

⇒99(x)³ = 0.334125

⇒ (x)³ = 0.003375

⇒ x = 0.015

Hence, numbers are 2(0.015) = 0.03

3(0.015) = 0.045

4(0.015) = 0.06