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