2013 AIME II Problem 1

Suppose that the measurement of time during the day is converted to the metric system so that each day has 10 metric hours, and each metric hour has 100 metric minutes. Digital clocks would then be produced that would read 9:99 just before midnight, 0:00 at midnight, 1:25 at the former 3:00 AM, and 7:50 at the former 6:00 PM. After the conversion, a person who wanted to wake up at the equivalent of the former 6: 36 \mathrm{Am} would set his new digital alarm clock for \mathrm{A}: \mathrm{BC}, where \mathrm{A}, \mathrm{B}, and \mathrm{C} are digits. Find 100 \mathrm{~A}+10 \mathrm{~B}+\mathrm{C}.