Question

A clock seen through a mirror shows ‘quarter to seven’. What is the correct time shown by the clock?

• A. 6:15
• B. 6:17
• C. 5:17
• D. 5:15

Answer 1

The Correct Option is D

To solve the problem of determining the correct time shown by a clock viewed through a mirror, we must understand how mirror images work for clocks. When you see a time in a mirror, each hand of the clock is mirrored horizontally across the vertical axis, which essentially transforms the mirror image to its symmetrical position on the real clock face. 

For a clock, we can determine the actual time from the mirror image using the following method:

1. Visualize a clock showing 12:00 and imagine how 6:00 would look in a mirror. This translates the numbers directly opposite their real position.
2. If the observed mirror image time is ‘quarter to seven’ (6:45), we need to find its actual opposite time on the clock when directly viewed.
3. To calculate this, first determine the reflected hour: 12 - 6 = 6. (Note: 12:00 - 6 = 6:00; the hour hand mirrors are simpler as it rotates directly opposite once categorized as AM or PM). This is because at 6 the reflects across the clock face to 6 as the central pivot point in this approach conveniently is an even number and middle marker.
4. Subtract the minutes from 60, as the mirror reflects them on the opposite half: 60 - 45 = 15. This compensates for the horizontal swap across half the clock face in reflecting.
5. From these calculations, the actual time is 5:15.

Thus, the correct time shown by the clock is 5:15.

Answer 2

The correct time shown by the clock is 5:15.

Additional Context:

• Mirror Time Concept:
  • Mirror images show time inverted horizontally
  • Subtract the mirrored time from 11:60 to get actual time
  • Formula: Actual Time = 11:60 - Mirrored Time
• Calculation:
  • Mirrored time: "quarter to seven" = 6:45
  • 11:60 - 6:45 = 5:15
• Verification method:
  • Draw clock hands at 5:15 and check its mirror image
  • Mirror of 5:15 appears as 6:45 ("quarter to seven")
• Alternative approach:
  • For times ≤6:00, add 6 hours to mirrored time
  • For times >6:00, subtract 6 hours from mirrored time
  • 6:45 >6:00 ⇒ 6:45 - 6:00 = 0:45 (12:45) → doesn't match options
  • Thus first method is more reliable
• Common mistakes:
  • Confusing "quarter to seven" (6:45) with "quarter past seven" (7:15)
  • Using 12:00 instead of 11:60 in calculations
  • Not accounting for the exact mirror inversion principle

Correct Answer: (4) 5:15.