Question

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

Answer 1

Hello dear user!

Let the numbers be 2x, 3x and 5x.

A/Q,

${(2x)}^{3} + {(3x)}^{3} + {(5x)}^{3} = 34560 \\ {8x}^{3} + {27x}^{3} + {125x}^{3} = 34560 \\ {160x}^{3} = 34560 \\ {x}^{3} = \frac{34560}{160} \\ {x}^{3} = 216 \\ x = \sqrt[3]{216} \\ x = 6$
So the numbers will be as follows,
First Number = 2 * 6 = 12
Second Number = 3 * 6 = 18
Third Number = 5 * 6 = 30

Hope it helps!