Question

The three numbers are in the ratio $1:2:3$ and the sum of their cubes is $98784$. The numbers are _____

• A. $(14,28,42)$
• B. $(6,12,18)$
• C. $(7,14,21)$
• D. $(8,16,24)$
• E. None of these

Answer 1

The correct option is A $(14,28,42)$

Ratio of three numbers$=1:2:3$

Let the numbers be $x,2x,3x$

Given that

$\Rightarrow x^3+(2x{)}^3+(3x{)}^3=98784$

$\Rightarrow x^3+8x^3+27x^3=98784$

$\Rightarrow 36x^3=98784$

$\Rightarrow x^3=2744$

$\Rightarrow x=14$

Therefore, numbers are $14,(14\times 2),(14\times 3)$

$\Rightarrow Numbers=(14,28,42)$