$(a)\;at \;origin \\ (b)\;+20 \;cm \\ (c)\;-20\;cm \\ (d)\;-10\;cm $

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From the y coordinates of the position of object and image we use that the magnification

$m= \large\frac{-2 cm}{1 cm} $$=-2$

image is real and inverted.

$\therefore |u| =x$

$|v| =2x$

Distance between object and image is

$50 -(-40)=90$

$\therefore x+2x= 90$

$3x= 90$

$x= 30$

distance of object from lens is 30 cm from lens.

$\therefore$ Distance of lens from origin is $-10\;cm$

Object is on other side with 60 cm from lens.

Hence d is the correct answer.

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