The determination of the boron isotopic ratio in solutions was achieved by means of a solid state track detector by using an alpha track. The neutron flux was optimized by using a Cd-foil to find the optimum conditions for counting the number of alpha tracks on the selected solid detector caused by the (n, $alpha$) nuclear reaction of boron. The home-made multi-dot detector plate was utilized in this study to increase the reproducibility of the measurement by uniformly drying the boron solution within the marked circle area on the detector plate. The experimental results of this study verified that the $^{11}B/^{10}B $ isotopic ratio can be measured by observing the number of alpha tracks for different concentrated standard solutions with various isotopic compositions. This technique was applied to the determination of $^{10}B$ enrichment factor in a biological sample for a boron neutron capture therapy.