Question : Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500. The smallest number is:
Option 1: 4
Option 2: 5
Option 3: 6
Option 4: 10
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Correct Answer: 5
Solution :
Let the numbers be $x, 2x$ and $3x$.
Cubes of the numbers are $x^3, 8x^3$ and $27x^3$.
According to the question,
$x^3 + 8x^3 + 27x^3 = 4500$
⇒ $36x^3 = 4500$
⇒ $x^3 = 125$
$\therefore x = 5$, which is the smallest number.
Hence, the correct answer is 5.
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