The pressure P and volume V of a gas are connected by the relation $PV^{1/4}=constant$. The percentage increase in the pressure corresponding to a deminition of $\dfrac12 \%$ in the volume is

$PV^{1/4}=constant$

$\displaystyle \Rightarrow P=\dfrac{k}{V^{{1}/{4}}}$

$\displaystyle \Rightarrow \dfrac{dP}{dV}=-\dfrac{k}{4}V^{-{5}/{4}}$

Percentage error in V $\displaystyle= -\dfrac{1}{2}\%$

$\Rightarrow\displaystyle \dfrac{\Delta V}{V} =-\dfrac{1}{200}$

$\Rightarrow\displaystyle {\Delta V}=-\dfrac{V}{200}$

Approximate change in $P\displaystyle=dP=(\dfrac{dP}{dV}){\Delta V}$

$\displaystyle =\dfrac{1}{800} {kV^{-1/4}}=\dfrac{1}{8}\%$ of P

Percentage increase in $V \ \displaystyle =\dfrac{1}{8}\%$