A point P divides the segment AB internally in the ratio 5 : 3, measured from A.
In what ratio does P divide the same segment when it is measured from B, that is, what is BP : PA?

AP : PB = 5 : 3 means AP is 5 parts and PB is 3 parts. Starting from B, the first piece met is BP = 3 parts and the second is PA = 5 parts, so BP : PA = 3 : 5 — the ratio simply reverses. Choosing 5 : 3 assumes the ratio is unchanged when the direction of reading is reversed; 3 : 8 and 8 : 5 compare one part with the WHOLE segment (5 + 3 = 8 parts) instead of part with part.