Question : The sum of the cube of two numbers in the ratio 3 : 4 is 5824. The sum of the numbers is:
Option 1: 5824
Option 2: 28
Option 3: 24
Option 4: 14
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Correct Answer: 28
Solution :
Let the numbers be $3x$ and $4x$.
Then $(3x)^3+(4x)^3 = 5824$
⇒ $27x^3+64x^3 = 5824$
⇒ $91x^3 = 5824$
⇒ $x^3 = 64$
$\therefore x= 4$
So, the sum of the numbers is = (3 × 4) + (4 × 4) = 12 + 16 = 28
Hence, the correct answer is 28.
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