We consider a two-way data exchanging system where a master node transfers energy and data packets to a slave node alternatively. The slave node harvests the transferred energy and performs information transmission as long as it has sufficient energy for current block, i.e., according to the best-effort policy. We examine the freshness of the received packets at the master node in terms of age of information (AoI), which is defined as the time elapsed after the generation of the latest received packet. We derive average uplink AoI and uplink data rate as functions of downlink data rate in closed form. The obtained results illustrate the performance limit of the unilaterally powered two-way data exchanging system in terms of timeliness and efficiency. The results also specify the achievable tradeoff between the data rates of the two-way data exchanging system.