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

Given: Three numbers are in the ratio of 2 : 3 : 5

The sum of their cubes is  34560

To do: Find the numbers

Solution:

Lets assume the numbers are  $2x,3x$ and $ 5x$

Sum of their cubes is 34560

$(2x)^3    +  (3x)^3   +  (5x)^3    =  34560$

$8x^3   +  27 x^3   +  125 x^3   =  34560$

$160 x ^3     =   34560$

$ x^3       =   \frac{34560}{ 160}$

 

$x^3       =  216$

$ x^3      =    6 \times 6 \times 6$

$ x   =  6$

Therefore, the numbers are 

$2(6)  ,  3(6)  ,  5(6)$

12 , 18 , 30