We analyse several outbursts of a few transient sources using Proportional Counter Array data (2.5-25 keV) as well as All Sky Monitor data (1.5-12 keV) of Rossi X-ray Timing Explorer satellite. We find a time delay between the arrival times of the Keplerian disc component and the halo of the Two-Component Advective Flow (TCAF) when the spectral data are fitted with TCAF solution. We compare this time delay from the spectral fits using the TCAF solution of the transient low-mass X-ray binaries (LMXBs) e.g. MAXI J1836-194, GX 339-4, and H 1743-322 during outbursts with that of the high-mass X-ray binary (HMXB) Cyg X-1 during its flares. We find that several days of time delays are observed in LMXBs while for Cyg X-1 the delay is negligible. We interpret the long delay to be due to the viscous time-scale of a large Keplerian component to reach the inner region as compared to nearly free-fall time taken by the low angular momentum halo component. The delay is of the order of a week for the LMXBs where the feeding is primarily through the Roche lobe. However, it is negligible in a wind-fed system like Cyg X-1 since a very small Keplerian disc is created here by slowly redistributing the low angular momentum of the wind and sporadic soft or intermediate spectral states are observed.