Maths / Cube and Cube Roots / Properties of Cubes of Numbers

QUESTION

Three numbers are in the ratio 2 : 3 : 5 to one another. The sum of their cubes is 54880. The numbers are _____ .

 OPTIONS A. 14, 21, 35 B. 12, 15, 17 C. 14, 18, 21 D. 21, 28, 32
Right Option : A

EXPLANATION
Explain TypeExplanation Content
Text

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

So, $(2x)^3+(3x)^3+(5x)^3=54880$

$\Rightarrow$  $8x^3 + 27x^3 + 125x^3 = 54880 \Rightarrow 160^3=54880$

$\Rightarrow$ $x^3 = \frac{54880}{160}=343 \Rightarrow x = 3\sqrt{343}=7$

So, numbers are 14, 21 and 35.

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