Three numbers are in the ratio 1 : 2 : 3 and the sum of

Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500 . The smallest number is

Let the numbers be x, 2x and 3x.
According to the question,
x³ + (2x)³ + (3x)³ = 4500
⇒ x³ + 8x³ + 27x³ = 4500
⇒ 36x³ = 4500

⇒ x³ =	4500	= 125
	36

∴ x³ = √125
= 5 = smallest number