The volume of the original solution that must be added can be calculated as following:
V = m / c
where V - volume of the solution, m - mass of DNA (50 pg), c - concentration of DNA solution.
As the concentration of DNA is 0.75mg/ml = 0.75 µg/µl and 1 pg = 1.0 × 10-6 µg:
V = 50 pg / 0.75mg/ml = 50 × 10-6 µg / 0.75 µg/µl = 6.7 × 10-5 µl
As a result, 6.7 × 10-5 µl of the original solution must be added.
As the template must be <10% of the PCR reaction volume (25 µl), than the volume of the DNA solution that can be added must be lower than 2.5 µl. For example, let assume that 1 µl of a template must be added. As the initial concentration of DNA is 0.75 µg/µl and the final concentration of DNA that is added into the PCR reaction is 50 pg/µl, the original sample must be diluted in 0.75 µg/µl / 50 pg/µl = 0.75 µg/µl / 50 × 10-6 µg/µl = 15000 times.
As a result, the dilution scheme is as following: