For $z=a^{2} x^{3} y^{\frac{1}{2}}$, where $a$ is a constant. If percentage error in measurement of $x$ and $y$ are $4 \%$ and $12 \%$, respectively, then the percentage error for $z$ will be $........... \%$

  • [JEE MAIN 2022]
  • A
    $18$
  • B
    $188$
  • C
    $78$
  • D
    $15$

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  • [AIIMS 2010]

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