An object is taken to a height above the surface of earth at a...

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

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

$⇒ {g}^{'} = \dfrac{g}{{\left(1 + \dfrac{1}{4}\right)}^{2}} = \dfrac{16}{25}g$

Change in weight

$∆ W = mg - m{g}^{'} ⇒ ∆ W = mg\left(1 - \dfrac{16}{25}\right)$

$⇒ ∆ W = \dfrac{9}{25}mg$

Percentage change $= \dfrac{9}{25} \times 100$

$= 36$