The non-destructive tests, such as rebound hammer (RH) and ultrasonic pulse velocity (UPV) tests, play a very important role in determining the quality and strength of the in-situ concrete without destruction. The present study aims to investigate the relationship between the destructive and non-destructive characteristics of the newly adopted alkaline (lime) activated recycled aggregate concrete containing ground granulated and granulated blast furnace slag (GGBFS and GBFS) obtained from steel industries. Eleven number of concrete sample mixes containing fixed percentage of GGBFS (60%) and lime (6%) along with the varying percentage (50, 75, and 100%) of GBFS and recycled coarse aggregate (RCA) obtained from demolition waste. The destructive (compressive strength) and non-destructive (RH and UPV) tests of these concrete mixes are conducted as per the relevant codes. The experimental outcomes of compressive strength (CS), rebound number (RN) and UPV show the similar trends. The UPV and RN of the concrete mix decrease with the increase in the GBFS and RCA content due to their inferior qualities as compared to NFA and NCA. It is found that the concrete mix with 60% GGBFS, 6% Lime, 50% or 75% GBFS, and 50% RCA show the comparable performance with respect to the normal concrete by reducing the equal amount of cement, NFA and NCA, which in turn makes the production of concrete sustainable. Moreover, it is found that UPV and RN are directly related to the compressive strength of these mixes with good correlation factor and hence, the compressive strength can be found out easily from UPV and RN without any destructive test like normal concrete.