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

Question:

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

Solution:

Let us assume the three number be a, 2a, 3a

Then,

Given, sum of cube of three numbers is 4500

i.e. a3 + (2a)3 + (3a)3 = 4500

a3 + 8a3 + 27a3 = 4500

36a3 = 4500

a3 = 4500/36

a3 = 125

a = 3√125

a = 3√(5 × 5 × 5)

a = 3√(53)

a = 5

∴The numbers are, a = 5

2a = 2 × 5 = 10

3a = 3 × 5 = 15

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