The sum of the cubes of two numbers in the ratio 3 : 4 is

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The sum of the cubes of two numbers in the ratio 3 : 4 is 5824. The sum of the numbers is :

Let the numbers be 3x and 4x.
According to the question,
(3x)³ + (4x)³ = 5824
⇒ 27x³ + 64x³ = 5824
⇒ 91x³ = 5824

⇒ x³ =	5824	= 64
	91

⇒ x = ³√64 = 4
∴ Sum of numbers
= 3x + 4x = 7x
= 7 × 4 = 28