Question

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

Answer 1

Ratio of three numbers = 2:3:5
Let the three numbers be 2x, 3x, and 5x. 
Given, 
Sum of their cubes = 34560
$(2x)^{3} + (3x)^{3} + (5x)^{2} = 34560$
$8x^{3} + 27x^{3} + 125x^{3} = 34560$
$160x^{3} = 34560$
$\frac{160x^{3} }{160} = \frac{34560}{160}$
$x^{3} = 216$
$\sqrt[3]{x^{3} } = \sqrt[3]{216}$
$x = 6$
Now, we know that the value of x is 6. 
We are going to find the numbers. 
2x = 2×6 = 12
3x = 3×6 = 18
5x = 5×6 = 30
Hence, the numbers are 12, 18, and 30. 

Answer 2

The answer is explained below.