Acceleration due to gravity at height $h$ is given by, $g^{\text{'}}=\frac{g}{{\left(1+\frac{h}{R}\right)}^2}$

For distance from the centre $r=\frac{5}{4}R$ height $h=\frac{R}{4}$,

$\Rightarrow g^{\text{'}}=\frac{g}{{\left(1+\frac{1}{4}\right)}^2}=\frac{16}{25}g$

Change in weight 

$$\begin{gathered} ∆W=mg-m{g}^{\text{'}} \\ \Rightarrow ∆W=mg\left(1-\frac{16}{25}\right) \end{gathered}$$

$\Rightarrow ∆W=\frac{9}{25}mg$

Percentage change $=\frac{9}{25}\times 100\%$

$=36\%$