Two point sources ${\mathrm{S}}_1 \mathrm{and} {\mathrm{S}}_2$ are 24 cm apart. Where a convex lens of focal length 9 cm be placed in between them so that the images of both sources are formed at the same place?

In this case one of the image will be real and the other virtual. Let us assume that image of ${\text{S}}_1$ is real and that of ${\text{S}}_2$ is virtual

$\mathrm{Applying}\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}}$

$\begin{array}{l}\mathrm{For}{\mathrm{S}}_1:\frac{1}{\mathrm{y}}+\frac{1}{\mathrm{x}}=\frac{1}{9}......\left(1\right)\\ \mathrm{for}{\mathrm{S}}_2:\frac{1}{\mathrm{y}}+\frac{1}{24-\mathrm{x}}=\frac{1}{9}...\left(2\right)\\ \mathrm{solving}\mathrm{equations}\left(1\right)\mathrm{and}\left(2\right),\mathrm{we}\mathrm{get}\mathrm{x}=6\mathrm{cm}\\ \mathrm{Note}:\mathrm{This}\mathrm{question}\mathrm{may}\mathrm{have}\mathrm{following}\mathrm{answer}6\mathrm{cm}\\ \mathrm{from}{\mathrm{S}}_1\mathrm{or}{\mathrm{S}}_2\mathrm{or}18\mathrm{cm}\mathrm{from}{\mathrm{S}}_2\mathrm{and}18\mathrm{cm}\mathrm{from}{\mathrm{S}}_1\mathrm{or}6\mathrm{cm}\mathrm{from}{\mathrm{S}}_2.\end{array}$