Question

Three no's. Are in a ratio of3:4:5 the sum of their cubes is 729000 .find the no.

Answer 1

Ratio of numbers → 3:4:5

Let the numbers be 3x, 4x and 5x respectively.

Now, as per the question, the sum of the cubes of the numbers is 729000.

${3x}^{3} + {4x}^{3} + {5x}^{3} = 729000$

= 27x^3 + 64x^3 + 125x^3 = 729000

$= {216x}^{3} = 729000$

$= 216x = \sqrt[3]{729000}$

= 216x = 90

= x = 90/216 = 10/24 = 5/12.