Question

Three numbers are in the ratio 1:2:3 and the sum of their cubes is 98784.
Find the numbers.

Answer 1

Let the $1x,2x\&3x$ are the 3 numbers

$\therefore$ sum of their cubes $=x^3+(2x{)}^3+(3x{)}^3$

$=98+84$

$=(36x{)}^3$

$x^3=\frac{98784}{36}=2274$

$x=\sqrt{2744}=14$

$\therefore 3$ numbers are $14,28,42$