Question

A concave lens of power 4D is placed at a distance of 40cm from 'O' at what distance from the lens should a candle be placed so that image formed on O'

Answer 1

There is a problem with the given data.  If it is a concave lens, then the power should be -4D.  Then further, the image cannot be formed at more than 25 cm from the lens.  Because for a concave lens , virtual image (small, erect) is formed within the focal length itself.

So the given lens is  BICONVEX lens.
Power = 1/f = +4D    => f = +100cm/4 = +25 cm
 
Lens formula:    1/v - 1/u = 1/f

case 1) We are expecting image to be virtual and on the same side as that of the object.
         v = -40 cm.   =>  -1/40 - 1/u = 1/25
     =>  u = -200/13 = -15.38 cm
     =>   m = v/u = -40/(-200/13) = 2.6

    Distance between O and the object:   | v - u | = 40 - 15.38 = 24.62 cm

case 2) the image at O is on the other side of the object.  So v = +40 cm
              1/40 - 1/u = 1/f = 1/25
               u = -200/3 cm = - 66.67 cm 
             The image is inverted and  magnification:  m = v/u = 40/(-200/3)
            m = - 0.6 
        Distance of the object from point O:  |u|+|v| = 40+66.67 = 106.67 cm