  The evolution of the C-type low frequency quasi-periodic oscillations
(LFQPOs) and associated time lag in transient black hole sources as a function
of time can be explained by variation of the Compton cloud size in a Two
Component Advective Flow solution (TCAF). A similar study of a persistent
source, GRS~1915+105, has not been attempted. We fit the evolution of QPOs with
propagatory oscillating shock (POS) solution for two sets of so-called
$\chi$-state observations and find that the shock steadily recedes with almost
constant velocity when QPO frequency is decreasing and the spectrum is
hardening. The shock moves inward with a constant velocity $v_0=473.0$ cm
s$^{-1}$ and $v_0=400.0$ cm s$^{-1}$ respectively in these two cases, when the
QPO frequency is increasing and the spectrum softens. This behavior is similar
to what was observed in XTE~J1550-564 during the 1998 outburst. The time lag
measured at the QPO frequency varies in a similar way as the size of the
Compton 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 irrespective
of the energy of photons. We find, at very low frequencies $< 1$ Hz, the
Comptonizing Efficiency (CE) increases with QPO frequency and at higher QPO
frequencies the trend is opposite. The time lags become mostly positive at all
energies when CE is larger than $\sim 0.85\%$ for both the sources.
