Ratio of size of the images in two positions
$\frac{I_{1}}{I_{2}}=\frac{3}{2}$
Distance of object from the screen, $D=?$
Applying formula,
${\frac{{{I_1}}}{{{I_2}}} = \frac{{{{(D + d)}^2}}}{{{{(D - d)}^2}}}}$
${ \Rightarrow \,\,\frac{3}{2} = \frac{{{{(D + 10)}^2}}}{{{{(D - 10)}^2}}}}$
${ \Rightarrow \quad \frac{3}{2} = \frac{{{D^2} + 100 + 20D}}{{{D^2} + 100 - 20D}}}$
$\Rightarrow 3 D^{2}+300-60 D=2 D^{2}+200+40 D$
$\Rightarrow \quad D^{2}-100 D+100=0$
On solving, we get $D=99\, \mathrm{cm}$
Hence the distance between the screen and the object is $99\, \mathrm{cm} .$
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