A body has maximum range R1  when projected up the inclined plane. The same body when projected down the inclined plane with same velocity it has maximum range R2. The maximum horizontal range for same velocity is

maximum range on inclined plane when projected up the plane=R1=u2g1+sinβ;  maximum range on inclined plane when projected down the plane=R2=u2g1−sinβ maximum range when projected on the ground=R =u2g  1R1+1R2=1u2g1+sinβ+1u2g1-sinβ 1R1+1R2=2gu2 1R1+1R2=2R R=2R1R2R1+R2