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