Three numbers are in the ratio $2 : 3 : 4$ to one another. The sum of their cubes is $33957$ . The numbers are _________.

14, 21, 28

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12, 15, 17

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14, 18, 21

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21, 28, 32

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Solution

The correct option is B $14, 21, 28$
let the numbers are $2 x . 3 x, 4 x$
the sum of their cubes
$= 8 x^{3} + 27 x^{3} + 64 x^{3}$ $= 33957$
$99 x^{3} = 33957$
$x^{3} = 343$
$x = 7$
so the numbers are $14, 21, 28$

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