Question

The three number are in the ratio 2:3:5.The sum of their cubes is 34560. Find the numbers

Answer 1

let the numbers be 2x,3x and 5x. Sum of their cubes is given 34560=>
${(2x)}^{3} + {(3x)}^{3} + {(5x)}^{3} = 34560$
$= > 8 {x}^{3} + 27 {x}^{3} + 125 {x}^{3} = 34560$
$160 {x}^{3} = 34560 = > {x}^{3} = \frac{34560}{160} = 216$
on keeping cube root on both sides,we get x=6.So the numbers is 12,18 and 30.