Physics Question on Ray optics and optical instruments

Question

A thin cylindrical rod of length $10\, cm$ is placed horizontally on the principle axis of a concave mirror of focal length $20 \,cm$ The rod is placed in a such a way that mid point of the rod is at $40 \,cm$ from the pole of mirror The length of the image formed by the mirror will be $\frac{x}{3} cm$ The value of $x$ is ______

Accepted Answer

The correct answer is 32.

UA=−45cm,f=−20cm
VA=−45−(−20)−45×(−20)=25−900=−36cm
And UB=−35cm
∴VB=−35−(−20)−35×(−20)=−15700
∴VA−VB= length of image
=(−36+3140)cm
=3−108+140cm
=332cm
∴x=32