Clock Problem of logic

Question

There is an analog clock that runs 90% of the normal speed of a clock.This clock will show the correct time exactly two times a day. Prove the following.

Answer 1

May be I am missing something, even if the clocks start synchronised, I don't see how they can show the same time again in the next $24$ hours.

The "bad" clock has to lose $12$ hours w.r.t. good one for the two to show the same time again.

Measuring by correct clock time,
In $10$ minutes, it loses $1$ minute.
In $10$ hours, it loses $1$ hour

To lose $12$ hours, it need $120$ hours of correct clock time $= 5\; days$

Answer 2

Without further information the claim is not true. Let the clock show $11:59$ when the correct time is $12:00$. The clock will only show the correct time once in the next $24$ hours.