Aclockseenthroughamirrorshows‘quartertoseven’. Whatisthecorrect time shown by the clock?

The correct option is 5:15.

To understand why this is the correct time, let's analyze the behavior of a mirror reflection of an analog clock. When a clock is reflected in a mirror, its left and right sides are reversed, while the top (12 o'clock) and bottom (6 o'clock) positions remain unchanged. This horizontal reflection means that a position on the clock face at $x$ hours corresponds to a reflected position of $12-x$ hours (or $11:60-\text{mirror time}$ when calculating with minutes).

Let's break down the given mirror time, which is "quarter to seven".
"Quarter to seven" is written digitally as 6:45.
In this position:
- The minute hand is pointing exactly at 9 (which represents 45 minutes).
- The hour hand is close to 7, slightly past the midway mark between 6 and 7.

Now, let's find the real time by reflecting these positions horizontally:
1. Minute Hand: The minute hand is at 9 (on the left side). Reflecting it horizontally across the vertical 12-6 axis moves it to 3 (on the right side). A minute hand pointing at 3 represents 15 minutes past the hour.
2. Hour Hand: The hour hand is just before 7. Reflecting this position across the vertical axis moves it to the corresponding position on the right side, which is just after 5 (since 7 is 1 unit past 6, its reflection is 1 unit before 6, which is 5). Thus, the hour hand points slightly past 5.

Alternatively, we can use the subtraction formula:
$\text{Actual Time}=11:60-6:45$
Subtracting the minutes:
$60-45=15$
Subtracting the hours:
$11-6=5$
This gives us the actual time of 5:15.