  Binary evolution leads to the formation of important objects crucial to 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 the 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 (CCF), we established a relationship between the derived mass ratio
and the PARs of the binary systems. By utilizing spectral observations obtained
from LAMSOT DR6 & 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 $0.6-1.0$ for investigating the mass-ratio
distribution. Through a power-law fitting, we obtained the power index $\gamma$
values of $-0.42\pm0.27$, $0.03\pm0.12$, and $2.12\pm0.19$ for 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 more in twins. The close binary fractions (for
$P\lesssim 150\,{\rm d}$ and $q\gtrsim 0.6$) in our sample for A, F and G
binaries are $7.6\pm 0.5 \%$, $4.9\pm 0.2 \%$ and $3.7 \pm 0.1 \%$,
respectively. Note that the PAR approach can be applied to large spectroscopic
surveys of stars.
