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The evolution of the C-type low frequency quasi-periodic oscillations(LFQPOs) and associated time lag in transient black hole sources as a functionof time can be explained by variation of the Compton cloud size in a TwoComponent Advective Flow solution (TCAF). A similar study of a persistentsource, GRS~1915+105, has not been attempted. We fit the evolution of QPOs withpropagatory oscillating shock (POS) solution for two sets of so-called$\chi$-state observations and find that the shock steadily recedes with almostconstant velocity when QPO frequency is decreasing and the spectrum ishardening. The shock moves inward with a constant velocity $v_0=473.0$ cms$^{-1}$ and $v_0=400.0$ cm s$^{-1}$ respectively in these two cases, when theQPO frequency is increasing and the spectrum softens. This behavior is similarto what was observed in XTE~J1550-564 during the 1998 outburst. The time lagmeasured at the QPO frequency varies in a similar way as the size of theCompton cloud. Most interestingly, in both the cases, the lag switches sign(hard lag to soft lag) at a QPO frequency of $\sim 2.3 - 2.5$ Hz irrespectiveof the energy of photons. We find, at very low frequencies $< 1$ Hz, theComptonizing Efficiency (CE) increases with QPO frequency and at higher QPOfrequencies the trend is opposite. The time lags become mostly positive at allenergies when CE is larger than $\sim 0.85\%$ for both the sources.

Evolution of Accretion Disc Geometry of GRS~1915+105 during its $\chi$ state as revealed by TCAF solution