Introduction
Mirror and water-image questions are common in reasoning tests. They ask you to read a clock when it is seen in a mirror (vertical reflection) or in water (horizontal reflection). These are geometry-of-reflection problems on the circular dial - they’re solved reliably by using a simple subtraction trick expressed in minutes.
Pattern: Mirror Image / Water Image
Pattern
Key concept: Treat the 12-hour clock as minutes on a 0-720 scale and use a fixed reference minute total to subtract the given time.
Mirror image (vertical reflection): subtract the given time from 12:00 (expressed as 720 minutes) - commonly remembered as the 11:60 - time rule.
Robust formula (minutes): MirrorTotal = 720 - GivenTotal (where GivenTotal = H×60 + M).
Convert MirrorTotal back to H:M (use 12 for 0 minutes).
Water image (horizontal reflection): subtract the given time from 18:30 (same as 17:90 notation). Robust formula (minutes): WaterTotal = 1,110 - GivenTotal. Convert WaterTotal back to H:M in 12-hour format (if result is 0 → 12:00).
Why these work: - The mirror (left-right) pairs numbers so the minute and hour positions add up to a fixed 12-hour total; subtracting from 720 (12 hours) gives the reflected dial reading. - The water (top-bottom) reflection pairs positions differently - subtracting from 18:30 (1,110 minutes) yields the horizontally inverted time.
Step-by-Step Example
Question
What is the mirror image and the water image of 3:20 (on a 12-hour analog clock)?
Solution
-
Step 1: Convert the given time to minutes
3:20 → GivenTotal = 3×60 + 20 = 200 minutes. -
Step 2: Mirror image - subtract from 720
MirrorTotal = 720 - 200 = 520 minutes. Convert: 520 ÷ 60 = 8 hours remainder 40 → 8:40. -
Step 3: Water image - subtract from 1,110 (18:30)
WaterTotal = 1,110 - 200 = 910 minutes. Convert to 12-hour: 910 - 720 = 190 → 190 ÷ 60 = 3 hours remainder 10 → 3:10. (Interpretation: 910 minutes = 15:10 on 24-hour scale → 3:10 PM on 12-hour dial.) -
Final Answer:
Mirror image = 8:40; Water image = 3:10 -
Quick Check:
Mirror: 3:20 mirrored horizontally should look like hour-hand near 8 and minute at 40 - matches 8:40 ✅
Water: top↔bottom flip of 3:20 places minute hand roughly near 2 and hour hand near 3 - 3:10 is consistent after normalization ✅
Quick Variations
• If minutes = 0, both formulas still work - normalise 0 minutes to 12:00 where needed (e.g., MirrorTotal = 720 - 180 = 540 → 9:00).
• Alternate notations you may encounter: 11:60 - time for mirror (same as 720 - time) and 17:90 or 18:30 for water (both equal 1,110 minutes). They are algebraic shorthands - use the total-minutes method for safety.
• If you get a result ≥720 minutes, subtract 720 to convert to 12-hour format.
Trick to Always Use
- Step 1 → Convert H:M to total minutes: Total = H×60 + M (treat 12 as 0 or 12×60 = 720 consistently).
- Step 2 → Mirror: compute 720 - Total. Water: compute 1,110 - Total.
- Step 3 → Convert the resulting minutes back to H:M. If result = 0 → 12:00; if ≥720 subtract 720 and then convert.
Summary
Summary
- Key takeaway 1: Mirror (vertical) time = 720 - given minutes → convert to H:M.
- Key takeaway 2: Water (horizontal) time = 1,110 - given minutes → convert to H:M (normalize to 12-hour clock if needed).
- Key takeaway 3: Equivalently, many sources write the mirror rule as
11:60 - timeand the water rule as18:30 - time(or17:90); these are shorthand forms of the minute totals above. - Key takeaway 4: Always convert to total minutes first, subtract, then normalize - this avoids sign/edge-case mistakes.
Example to remember:
Mirror: Mirror(3:20) = 720 - 200 = 520 → 8:40.
Water: Water(3:20) = 1,110 - 200 = 910 → 910 - 720 = 190 → 3:10.
Hint: Mirror image = 11:60 - given time.
Common Mistakes: Adding instead of subtracting from 12:00.