Let the amount saved by the brother that has less savings be x, then the savings of the other brother is x + 15.
Since their total savings is 55, then
x + x + 15 = 55
2x + 15 = 55
2x = 55 - 15 = 40
x = 40 / 2 = 20
Therefore, one person saved 20 and the other saved 20 + 15 = 35.