We have recently presented observational evidence which suggests that the origin of the second-generation (G2) stars in globular clusters (GCs) is due to the binary-mediated collision of primordial (G1) low-mass main-sequence (MS) stars. This mechanism avoids both the mass budget problem and the need of external gas for dilution. Here, we report on another piece of evidence supporting this scenario: (1) the fraction of MS binaries is proportional to the fraction of G1 stars in GCs and, at the same time, (2) the smaller the fraction of G1 stars is, the more deficient binaries of higher mass ratio (q>0.7) are. They are, on average, harder than their smaller mass-ratio counterparts due to higher binding energy at a given primary mass. Then (2) implies that (1) is due to the merging/collisions of hard binaries rather than to their disruption. These new results complemented by the present-day data on binaries lead to the following conclusions: (i) the mass-ratio distribution of binaries, particularly short-period ones, with low-mass primaries, M-P < 1.5 M-circle dot, is strongly peaked close to q=1.0, whereas (ii) dynamical processes at high stellar density tend to destroy softer binaries and make hard (nearly) twin binaries to become even harder and favour their mergers and collisions. G2 stars formed this way gain mass that virtually doubles the primary one, 2M(P), at which the number of G1 stars is approximately five times smaller than at M-P according to the slope of a Milky Way-like initial mass function at M-MS < 1.0 M-circle dot.