Consider a lens and a small object placed at right angles to its optic axis at a position A such that the image formed is six times magnified. The object is now shifted away from the lens to another position B at a distance 12 cm from position A and an image that is magnified two times but of the same nature as in earlier case, is obtained. Shifting the position of the object from B to a third position C results in an image that is 4 times reduced in size. At all positions so far, length of the object is kept perpendicular to the optic axis.

Find the distance of position A and B of the object from the optic centre and the focal length of the lens.