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

Solution (By Examveda Team)

$$\eqalign{ & x:2x:3x \cr & {x^3} + 8{x^3} + 27{x^3} = 4500 \cr & 36{x^3} = 4500 \cr & {x^3} = \frac{{4500}}{{36}} = 125 \cr & x = 5 \cr & {\text{Smallest number is 5}} \cr} $$