We present new Atacama Large Millimeter/sub-millimeter Array (ALMA) 1.3 mm continuum observations of the SR 24S transition disk with an angular resolution less than or similar to 0'.18 (12 au radius). We perform a multi-wavelength investigation by combining new data with previous ALMA data at 0.45 mm. The visibilities and images of the continuum emission at the two wavelengths are well characterized by a ring-like emission. Visibility modeling finds that the ring-like emission is narrower at longer wavelengths, in good agreement with models of dust-trapping in pressure bumps, although there are complex residuals that suggest potentially asymmetric structures. The 0.45 mm emission has a shallower profile inside the central cavity than the 1.3 mm emission. In addition, we find that the (CO)-C-13 and (CO)-O-18 (J = 2-1) emission peaks at the center of the continuum cavity. We do not detect either continuum or gas emission from the northern companion to this system (SR 24N), which is itself a binary system. The upper limit for the dust disk mass of SR 24N is less than or similar to 0.12 M-circle plus, which gives a disk mass ratio in dust between the two components of M-dust,M-SR 24S/M-dust,M-SR 24N greater than or similar to 840. The current ALMA observations may imply that either planets have already formed in the SR 24N disk or that dust growth to millimeter sizes is inhibited there and that only warm gas, as seen by rovibrational CO emission inside the truncation radii of the binary, is present.