If $x$ and $y$ are in inverse proportion with constant $xy = k$, and we replace $x$ by $2x$ and $y$ by $3y$,…

If $x$ and $y$ are in inverse proportion with constant $xy = k$, and we replace $x$ by $2x$ and $y$ by $3y$, the new product equals:
  1. $k$
  2. $2k$
  3. $5k$
  4. $6k$

Solution

New product $= (2x)(3y) = 6 xy = 6k$.

Asked in: IMO

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