An object is placed on the principal axis of convex lens of focal...

Given here: Focal length of convex lens, $f = 10cm$

Now, as seen in figure, image from lens is formed at point ${I}_{1}$, whose location is $5cm$ from mirror. Thus, ${I}_{1}$ is at $15cm$ from lens.

Using lens equation, we have

$\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$

Putting the value,

$\dfrac{1}{15} - \dfrac{1}{- u} = \dfrac{1}{10}$

$⇒ \dfrac{1}{u} = \dfrac{1}{10} - \dfrac{1}{15} ⇒ u = \dfrac{10 \times 15}{10 - 15}$

Thus, object is placed at $30cm$ from lens.