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 = 3sqrt{343}=7

So, numbers are 14, 21 and 35.

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