On a mercator:
Scale = Chart distance/Earth distance = Scale at equator x 1 /cos lat
Transpose: Chart distance = (Scale at equator x Earth distance)/cos lat
Since it is the same chart distance at 15ºS and 10ºN:
(Scale at equator x Earth dist. at 15ºS)/cos 15º =
(Scale at equator x Earth dist at 10ºS)/cos 10º
Or: ED at 15º/cos 15º = ED at 10º/cos
10º
ED at 10º = (ED at 15º x cos 10º)/Cos 15º = (120 x
.985)/.966 = 122.3nm