Transport of droplets on surfaces is important for a variety of applications such as micro liquid handling and biochemical assays. In the present work, we study evaporation-induced attraction, chasing and repulsion between a target pure aqueous (water) droplet and a driver aqueous mixture droplet comprising water and a lower surface tension and lower vapour pressure liquid on a high energy surface. It is observed that for a fixed concentration of mixture droplet, attraction/chasing or repulsion can be achieved by varying the relative time instants at which the drops are dispensed. Our study reveals that if the water droplet is dispensed within a critical time after dispensing the mixture droplet, the latter will get attracted to and chase the water droplet. On the other hand, if the water droplet is dispensed after this critical time, then it would get repelled from the mixture droplet. We explain the underlying mechanisms that govern the phenomena and demonstrate continuous transport of liquid/cell sample droplets/plugs.