Question

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

Answer 1

Suppose the three numbers be x, 2x, 3x

Given: Sum of cube of three numbers is 4500.

x³ + (2x)³ + (3x)³ = 4500

x³ + 8x³ + 27x³ = 4500

36x³ = 4500

x³ = `4500/36`

x³ = 125

x = `root(3)(125)`

x = `root(3)(5 xx 5 xx 5)`

x = `root(3)(5^3)`

x = 5

So, the numbers are, x = 5,

2a = 2 × 5 = 10

3a = 3 × 5 = 15