Question

ii) Three numbers are in the ratio 1: 2: 3 and the cube of their sum is 1728. Find the
numbers​

Answer 1

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

Their sum = x + 2x + 3x = 6x

Cube of their sum = (6x)³ = 216x³

According to question,

216x³ = 1728

${\sf{\implies\: x^{3}\: =\: {\dfrac{1728}{216}}}}$

${\sf{\implies\: x^{3}\: =\: 8}}$

${\sf{\implies\: x\: =\: \sqrt[3]{8}}}$

${\sf{\implies\: x\: =\: \bold{2}}}$

Now,

1st no. = x = 2

2nd no. = 2x = 2 × 2 = 4

3rd no. = 3x = 3 × 2 = 6

${\bold{\boxed{\fcolorbox{blue}{ink}{Required\: numbers\: are\: 2\: ,\:4\: and\: 6}}}}$