Question

Three numbers are in the ratio 1 : 2 : 3. The sum of their cubes is 98784. Find the numbers.

• A. 14, 20 and 50
• B. 14, 28 and 42
• C. 17, 42 and 28
• D. 14, 28 and 25

Answer 1

The correct option is B 14, 28 and 42

Let the numbers are x, 2x and 3x.
$Given:x^3+(2x{)}^3+(3x{)}^3=98784$
$\Rightarrow x^3+8x^3+27x^3=98784$
$\Rightarrow 36x^3=98784$
$\Rightarrow x^3=\frac{98784}{36}=2744$
$\Rightarrow x^3=14\times 14\times 14$
$\Rightarrow x=\sqrt[3]{314\times 14\times 14}=14$
$\Rightarrow 2x=28$ and $3x=42$.
$\therefore$ The required numbers are 14, 28 and 42.