$(a)\;12\;cm \\ (b)\;72\;cm \\ (c)\;18\;cm \\ (d)\;36\;cm $

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$\large\frac{1}{3x}+\frac{1}{x} =\frac{1}{f}$

or $\large\frac{4}{3x} =\frac{1}{f}$ -----(i)

$\large\frac{1}{2(6+x)}+\frac {1}{6+x} =\frac{1}{f}$

ot $\large\frac{3}{2(6+x)} =\frac {1}{f}$-----(ii)

from equation (i) and (ii) , it gives

$\large\frac{4}{3x} =\frac{3}{2(6+x)}$

$\therefore 9x= 48+8x$

$x=48 \;cm$

Shift of screen $=3x-2(6+X)$

$\qquad= 3 \times 48 -2 (6+ 48)$

$\qquad=36 \;cm$

Hence d is the correct answer.

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