Thanks for the response to this puzzle. I got correct answers from three people – Ashutosh Diwakar, Rajeev Deshpande and Pallav Pandey in that order. Well done!

I am also taking the liberty of replicating Ashotosh’s solution which I thought was very well explained. If you want to use a video for children, you can access it on the following link:

https://www.educreations.com/lesson/view/solution-to-puzzle-75/24663132/?s=7LLAbY&ref=app

The answer is 27 minutes and 41 seconds past the hour after 6 pm.

Puzzle 75 Solution

In one hour or 60 minutes of duration, hour hand is shifted or advanced by 5 minutes.

So, let’s suppose after 6 o’clock, it takes another x minutes to reach the condition mentioned in question i.e.  reflection should show the same timing.

Then,

In 60 min., hour hand is advanced by = 5 min.

In x min., hour hand will be advanced by = (5/60)*x min.

Now, at this time w.r.t. 6 o’clock, minute hand will be back by = (30-x) min.

From the question, the time by which the hour hand is advanced should be equal to the time by which minute hand is back:

=>           (5/60)*x = (30-x)

=>           x = (27+9/13)min.

Therefore, (27+9/13)min. after 6 o’clock, the reflection in the mirror will show the same timing.