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Mirror Image / Water Image

Introduction

Mirror और water-image वाले questions reasoning tests में बहुत common होते हैं। इनमें clock को mirror (vertical reflection) में या पानी में (horizontal reflection) देखने पर क्या time दिखेगा, यह निकालना होता है। यह circular dial पर reflection-geometry का concept है - इसे एक simple subtraction trick से minutes में बहुत आसानी से solve किया जाता है।

Pattern: Mirror Image / Water Image

Pattern

Key concept: 12-hour clock को 0-720 minutes scale की तरह treat करें और given time को एक fixed reference minute-total से subtract करें।

Mirror image (vertical reflection): Given time को 12:00 (720 minutes) में से subtract करें - जिसे अक्सर 11:60 - time rule के रूप में याद रखा जाता है। Robust formula (minutes): MirrorTotal = 720 - GivenTotal (जहाँ GivenTotal = H×60 + M). MirrorTotal को वापस H:M में बदलें (0 minutes आए तो 12 लिखें)।

Water image (horizontal reflection): Given time को 18:30 (या 17:90 notation) में से subtract करें। Robust formula (minutes): WaterTotal = 1,110 - GivenTotal. WaterTotal को 12-hour format में वापस बदलें (result 0 आए तो 12:00 लिखें)।

Why these work: - Mirror (left-right) reflection में hour और minute positions का sum हमेशा एक fixed 12-hour total होता है; इसलिए 720 में से subtract करने पर mirrored reading मिलती है। - Water (top-bottom) reflection में dial का pairing अलग होता है - इसलिए 18:30 (1,110 minutes) में से subtract करना सही reflected-time देता है।

Step-by-Step Example

Question

12-hour analog clock पर 3:20 का mirror image और water image क्या होगा?

Solution

  1. Step 1: Given time को minutes में बदलें

    3:20 → GivenTotal = 3×60 + 20 = 200 minutes.

  2. Step 2: Mirror image - 720 में से subtract करें

    MirrorTotal = 720 - 200 = 520 minutes. Convert: 520 ÷ 60 = 8 hours remainder 40 → 8:40.

  3. Step 3: Water image - 1,110 में से subtract करें

    WaterTotal = 1,110 - 200 = 910 minutes. 12-hour format में बदलें: 910 - 720 = 190 → 190 ÷ 60 = 3 hours remainder 10 → 3:10. (Interpretation: 910 minutes = 15:10 → 12-hour dial पर 3:10 PM)

  4. Final Answer:

    Mirror image = 8:40; Water image = 3:10

  5. Quick Check:

    Mirror: 3:20 का mirror-hour लगभग 8 और minute 40 दिखना चाहिए - 8:40 सही है ✅
    Water: top↔bottom flip में minute-hand लगभग 2 के पास और hour-hand 3 के पास जाता है - 3:10 सही निकलता है ✅

Quick Variations

• अगर minutes = 0 हो, तब भी formula सही चलता है - जैसे MirrorTotal = 720 - 180 = 540 → 9:00।

• Alternate notations: 11:60 - time mirror के लिए (same as 720 - time) और 17:90 या 18:30 water के लिए (दोनों 1,110 minutes के बराबर)। ये algebraic shorthands हैं - safest तरीका वही total-minutes method है।

• Result ≥720 minutes आए तो 720 subtract करके normal 12-hour time में बदलें।

Trick to Always Use

  • Step 1 → H:M को minutes में बदलें: Total = H×60 + M (12 को 0 या 12×60 = 720 मानकर consistent रहें)।
  • Step 2 → Mirror: 720 - Total. Water: 1,110 - Total.
  • Step 3 → Result को वापस H:M में बदलें। Result = 0 हो तो 12:00 लिखें; ≥720 हो तो पहले 720 subtract करें।

Summary

Summary

  • Key takeaway 1: Mirror (vertical) time = 720 - given minutes → H:M में convert करें।
  • Key takeaway 2: Water (horizontal) time = 1,110 - given minutes → H:M में convert करें (12-hour format में normalize करें)।
  • Key takeaway 3: कई sources mirror rule को 11:60 - time और water rule को 18:30 - time (या 17:90) लिखते हैं - यह उसी minute-total method का shorthand है।
  • Key takeaway 4: हमेशा पहले minutes में convert करें, subtract करें, फिर normalize करें - इससे mistakes नहीं होतीं।

याद रखने लायक example:
Mirror: Mirror(3:20) = 720 - 200 = 520 → 8:40.
Water: Water(3:20) = 1,110 - 200 = 910 → 910 - 720 = 190 → 3:10.

Practice

(1/5)
1. If a clock shows 2:15, what will be its mirror image time?
easy
A. 9:45
B. 9:50
C. 10:45
D. 9:35

Solution

  1. Step 1: Convert to total minutes

    2:15 → (2×60) + 15 = 135 minutes.

  2. Step 2: Mirror formula

    MirrorTotal = 720 - 135 = 585 minutes.

  3. Step 3: Convert back to H:M

    585 ÷ 60 = 9 hours remainder 45 → 9:45.

  4. Final Answer:

    9:45 → Option A

  5. Quick Check:

    2:15 reflected around 12:00 should read 9:45 ✅
Hint: Mirror image = 11:60 - given time.
Common Mistakes: Adding instead of subtracting from 12:00.
2. What is the mirror image of 7:40 on a 12-hour analog clock?
easy
A. 5:40
B. 4:20
C. 3:50
D. 4:10

Solution

  1. Step 1: Convert to total minutes

    7:40 → (7×60) + 40 = 460 minutes.

  2. Step 2: Mirror formula

    MirrorTotal = 720 - 460 = 260 minutes.

  3. Step 3: Convert back to H:M

    260 ÷ 60 = 4 hours remainder 20 → 4:20.

  4. Final Answer:

    4:20 → Option B

  5. Quick Check:

    7:40 + 4:20 = 12:00 - works perfectly ✅
Hint: For mirror, subtract given time from 12:00.
Common Mistakes: Not converting total minutes properly.
3. If a clock shows 11:10, what will be its mirror image time?
easy
A. 12:55
B. 1:10
C. 12:50
D. 12:45

Solution

  1. Step 1: Convert to total minutes

    11:10 → (11×60) + 10 = 670 minutes.

  2. Step 2: Mirror formula

    MirrorTotal = 720 - 670 = 50 minutes.

  3. Step 3: Convert back to H:M

    50 ÷ 60 = 0 hours remainder 50 → 12:50 (0:50 → 12:50).

  4. Final Answer:

    12:50 → Option C

  5. Quick Check:

    11:10 mirrored should be 12:50 (sum to 12:00 with wrap) ✅
Hint: If mirror time < 60 min, hour = 12.
Common Mistakes: Forgetting that 0 hours converts to 12:00.
4. What will be the water image of 2:45?
medium
A. 9:45
B. 3:45
C. 9:15
D. 3:15

Solution

  1. Step 1: Convert to total minutes

    2:45 → (2×60) + 45 = 165 minutes.

  2. Step 2: Apply Water Image Formula

    Water image = 18:30 - given time (in minutes).
    Convert 18:30 → (18×60) + 30 = 1,110 minutes.
    WaterTotal = 1,110 - 165 = 945 minutes.

  3. Step 3: Convert back to 12-hour format

    945 - 720 = 225 minutes → 225 ÷ 60 = 3 hours remainder 45 → 3:45.

  4. Final Answer:

    3:45 → Option B

  5. Quick Check:

    Water image flips top↔bottom - for 2:45, the correct reflected reading is 3:45 ✅
Hint: Use 18:30 (1,110 minutes) - given time; convert total back to 12-hour format.
Common Mistakes: Confusing mirror image (11:60 - time) with water image (18:30 - time).
5. Find the mirror image of 4:50 on a clock dial.
medium
A. 7:10
B. 7:20
C. 6:40
D. 8:00

Solution

  1. Step 1: Convert to total minutes

    4:50 → (4×60) + 50 = 290 minutes.

  2. Step 2: Mirror formula

    MirrorTotal = 720 - 290 = 430 minutes.

  3. Step 3: Convert back to H:M

    430 ÷ 60 = 7 hours remainder 10 → 7:10.

  4. Final Answer:

    7:10 → Option A

  5. Quick Check:

    4:50 + 7:10 = 12:00 (mirror check) ✅
Hint: Mirror image = 12:00 - given time (convert minutes properly).
Common Mistakes: Using 12:60 instead of 11:60 convention.

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