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Question 62
The ratio of two numbers is 4 : 5 and the sum of their cubes is 1512. The square of their difference is:
Solution
Let the two numbers be 4x and 5x
Sum of their cubes = $$4x^3 + 5x^3 = 64x^3 + 125x^3 = 189x^3$$
Given, $$189x^3 = 1512 => x^3 = 8 => x = 2$$
Then, Two numbers are 4x = 4*2 = 8 and 5x = 5*2 = 10
Therefore, Square of their difference = $$(10-8)^2 = 2^2 = 4$$
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