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# 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**

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