Binary evolution leads to the formation of important objects that are crucial for the development of astrophysics, but the statistical properties of binary populations are still poorly understood. The LAMOST-MRS has provided a large sample of stars to study the properties of binary populations, especially for the mass-ratio distributions and binary fractions. We have devised a peak amplitude ratio (PAR) approach to derive the mass ratio of a binary system based on results obtained from its spectrum. By computing a cross-correlation function, we established a relation between the derived mass ratio and the PARs of the binary systems. By using spectral observations obtained from LAMSOT DR6 and DR7, we applied the PAR approach to form distributions of the derived mass ratio of the binary systems to the spectral types. We selected the mass ratio within the range of 0.6-1.0 to investigate the mass-ratio distribution. Through a power-law fitting, we obtained power index gamma values of -0.42 +/- 0.27, 0.03 +/- 0.12, and 2.12 +/- 0.19 for the A-, F-, and G-type stars identified in the sample, respectively. The derived gamma-values display an increasing trend toward lower primary star masses, and G-type binaries tend to be twins more frequently. The close binary fractions (for P less than or similar to 150 days and q greater than or similar to 0.6) in our sample for A, F, and G binaries are 7.6% +/- 0.5%, 4.9% +/- 0.2%, and 3.7% +/- 0.1%, respectively. Note that the PAR approach can be applied to large spectroscopic surveys of stars.