Due to financial difficulties, Mariana asked her boss for an advance on her 13th salary twice in a year. The first advance was 3/7 of the value of the 13th, and the second, 2/5 of the value of the remainder of the 13th. So the fraction that represents the remainder of Mariana's 13th is:

First advance: (3/7)x This leaves a remainder of x - (3/7)x = (4/7)x. Second advance: (2/5) * ((4/7)x) = (8/35)x So, the remainder of Mariana's 13th salary after both advances is: (4/7)x - (8/35)x = (20/35)x - (8/35)x = (12/35)x. Therefore, the fraction that represents the remainder of Mariana's 13th salary is 12/35.