The apparent weight of a person inside a lift is${\text{w}}_{\text{1}}$ when lift moves up with a certain acceleration and is${\text{w}}_{\text{2}}$ when lift moves down with same acceleration. The weight of the person when lift moves up with constant speed is

When the lift is moving down with constant acceleration upwards we get the equation as

$\text{mg}-\text{ma}={\text{w}}_{\text{1}}\to \left(1\right)$

And when moving up with same acceleration we get${\text{w}}_{\text{2}}$ ,

$\text{mg}+\text{ma}={\text{w}}_{\text{2}}\to \left(2\right)$

While lift is moving down with constant speed there is no external force except the gravitational force so then we will get the weight of the person

Now add (1) + (2)

$\text{mg}-\text{ma}+\text{mg}+\text{ma}={\text{w}}_{\text{1}}+{\text{w}}_{\text{2}}$

$2\text{mg}={\text{w}}_{\text{1}}+{\text{w}}_{\text{2}}$

$\text{mg}=\frac{{\text{w}}_{\text{1}}+{\text{w}}_{\text{2}}}{2}$

$\text{w}=\frac{{\text{w}}_{\text{1}}+{\text{w}}_{\text{2}}}{2}$