Aman goes 35m due west and 12m due north . how far is he from the starting point?

Think of this as a coordinate on a Cartesian plane. You have the origin, which is (0,0), and then you have this vector traveled, (35,12). The 35 should ideally be negative, however, when speaking in terms of distance, negatives are irrelevant. So now use the distance formula to find the distance between the two points.
D = sqrt[ (x2-x1)^2 + (y2-y1)^2 ]
D = sqrt[ 1225 + 144 ]
D = sqrt[ 1369 ]
D = 37m