Question

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

Answer 1

Ratio in numbers = 1 : 2 : 3
Let first number = x
Then second number = 2x
and third number = 3x
$\therefore$ Sum of cubes of there numbers $=(x{)}^3+(2x{)}^3+(3x{)}^3\therefore x^3+8x^3+27x^3=98784\Rightarrow 36x^3=98784\therefore x^3=\frac{98784}{36}=2744x=3\sqrt{2744}$

$=3\sqrt{2\times 2\times 2\times 7\times 7\times 7}=3\sqrt{2^3\times 7^3}=2\times 7=14$
Number will be $14,2\times 14,3\times 14$ i.e. 14, 28, 42