# Equi convex lens is placed such that optic axis coincides with the x-axis, position of object is $(-40 \;cm, 1 \;cm)$ and position of image $(50 \;cm, -2\;cm)$ where is the lens located

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

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.