A simple spectrophotometric method has been developed for resolving binary mixtures of Rhodamine B and Rhodamine 6G dyes of red ballpoint pen ink using the first-derivative spectra with measurements at zero-crossing wavelengths. Calibration graphs were linear up to 8 mg L-1 for Rhodamine B and 10 mg L-1 for Rhodamine 6G. This method was successfully applied for the quantitative determination of dyes having overlapping spectra in their bi-component mixtures. The applied derivative method is practical, simple, rapid, inexpensive and suitable for quantitative analysis of bi-component dye solutions in the ballpoint pen ink.