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A number when divided by $9$ gives the perfect cube of $6$ and when multiplied by $3$ gives another perfect cube of $18$. Find the number.
Given: A number when divided by $9$ gives the perfect cube of $6$ and when multiplied by $3$ gives another perfect cube of $18$.
To do: To find the number.
Solution:
Let $x$ be the number.
As given, when the number is divided by $9$ gives the perfect cube of $6$
$\Rightarrow \frac{x}{9}=6^3=6\times6\times6=216$
$\Rightarrow x=216\times9$
$\Rightarrow x=1944$
If we multiply the number by $3$, it becomes the cube of $18$.
$\Rightarrow 3x=18^3=18\times18\times18=5832$
$\Rightarrow x=\frac{5832}{3}$
$x=1944$
Therefore, $x=1,944$.
Updated on: 10-Oct-2022
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