SSC CGL Tier 1 Reasoning: Clock - 20 Practice MCQs with Solutions

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Clock Reasoning Questions for SSC CGL 2025: 20 Practice MCQs with Solutions | Angle, Mirror Image & Faulty Clock

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Practice 20 Clock Reasoning MCQs for SSC CGL Tier 1 with detailed solutions. Covers angle between hands, mirror/water image, faulty clocks, coinciding hands & more. Easy, Medium, Hard levels. Free PDF!

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Are you preparing for SSC CGL Tier 1 and finding Clock reasoning questions tricky? Clock problems are a favorite among examiners and appear regularly in the Reasoning section. Master this topic and score easy marks!

Clock reasoning tests your understanding of how clock hands move, the angles they make, and concepts like mirror images and faulty clocks. In this comprehensive practice set, we bring you 20 carefully designed MCQs covering all important sub-topics:

• Angle Between Hands – Calculate exact angle at any given time

• Coinciding Hands – When do hour and minute hands overlap?

• Right Angle & Straight Line – 90° and 180° positions

• Mirror Image of Clock – Time shown in reflection

• Water Image of Clock – Upside-down reflections

• Faulty/Gaining/Losing Clocks – Clocks that run fast or slow

• Direction Based Problems – Clock hands pointing to compass directions

Each question includes detailed step-by-step explanations with formulas and calculations. Whether you're a beginner or looking to perfect your skills, this set covers Easy, Medium, and Hard difficulty levels.

Key Formulas You'll Master:

• Angle = |30H - 5.5M| or |30H - 11M/2|

• Minute hand speed: 6° per minute

• Hour hand speed: 0.5° per minute

• Relative speed: 5.5° per minute

• Mirror image: 11:60 - given time

Download the free PDF and boost your SSC CGL Reasoning score today!

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Full Version: SSC CGL Tier 1 Reasoning Clock practice questions PDF containing 20 MCQs with detailed step-by-step explanations, covering angle between hands, coinciding hands, right angle problems, mirror and water image, faulty clocks, and direction-based clock problems across easy, medium, and hard difficulty levels for government exam preparation.

Short Version: SSC CGL Clock Reasoning 20 MCQs PDF with solutions - Easy, Medium, Hard levels

📝 Practice Questions

SECTION: EASY LEVEL

Q1. How many times do the hands of a clock coincide (overlap) in a day (24 hours)?

(A) 22    (B) 24    (C) 44    (D) 48

✓ Correct Answer: (A) 22

Explanation:

• Step 1: In 12 hours, the minute hand completes 12 rounds while the hour hand completes 1 round.

• Step 2: Relative rounds = 12 - 1 = 11 rounds

• Step 3: So the hands coincide 11 times in 12 hours.

• Step 4: In 24 hours = 11 × 2 = 22 times

• Note: The hands coincide at 12:00, but this is counted only once for each 12-hour period.

Q2. What is the angle between the hour hand and minute hand at 3:00?

(A) 60 degrees    (B) 75 degrees    (C) 90 degrees    (D) 120 degrees

✓ Correct Answer: (C) 90 degrees

Explanation:

• Step 1: At 3:00, the minute hand is at 12 (0 degrees) and the hour hand is at 3.

• Step 2: Each hour mark represents 30 degrees (360°/12 = 30°).

• Step 3: The hour hand at 3 = 3 × 30 = 90 degrees from 12.

• Step 4: Angle between hands = 90 - 0 = 90 degrees

Q3. At what time between 2 and 3 o'clock will the hands of a clock be together (coincide)?

(A) 2:10 10/11    (B) 2:10    (C) 2:11    (D) 2:10 5/11

✓ Correct Answer: (A) 2:10 10/11

Explanation:

• Step 1: At 2:00, the hour hand is at 60 degrees (2 × 30).

• Step 2: For hands to coincide, minute hand must catch up 60 degrees.

• Step 3: Relative speed = 6 - 0.5 = 5.5 degrees per minute.

• Step 4: Time = 60 ÷ 5.5 = 60 × 2/11 = 120/11 = 10 10/11 minutes

• Step 5: So the hands coincide at 2:10 10/11

Q4. How many times are the hands of a clock at right angle in a day?

(A) 22    (B) 24    (C) 44    (D) 48

✓ Correct Answer: (C) 44

Explanation:

• Step 1: In 12 hours, the hands are at right angle (90 degrees) 22 times.

• Step 2: This is because they make 90° twice in most hours, but between 2-4 and 8-10, one instance is shared.

• Step 3: In 24 hours = 22 × 2 = 44 times

Q5. What is the angle between the hands of a clock at 6:30?

(A) 0 degrees    (B) 15 degrees    (C) 30 degrees    (D) 45 degrees

✓ Correct Answer: (B) 15 degrees

Explanation:

• Step 1: Use formula: Angle = |30H - 5.5M|

• Step 2: H = 6, M = 30

• Step 3: Angle = |30 × 6 - 5.5 × 30|

• Step 4: Angle = |180 - 165| = 15 degrees

Q6. A clock shows 3:15. What is the time shown if we see its reflection in a mirror?

(A) 8:45    (B) 9:45    (C) 8:15    (D) 9:15

✓ Correct Answer: (A) 8:45

Explanation:

• Step 1: Mirror image formula: Subtract from 11:60 (or 12:00).

• Step 2: For time before the minute is 00-30: Mirror time = 11:60 - given time.

• Step 3: Mirror time = 11:60 - 3:15 = 8:45

• Alternative: The hands swap positions horizontally. 3:15 in mirror shows 8:45.

Q7. At what angle are the hands of a clock inclined at 15 minutes past 5?

(A) 58.5 degrees    (B) 64 degrees    (C) 67.5 degrees    (D) 72.5 degrees

✓ Correct Answer: (C) 67.5 degrees

Explanation:

• Step 1: Use formula: Angle = |30H - 5.5M|

• Step 2: H = 5, M = 15

• Step 3: Angle = |30 × 5 - 5.5 × 15|

• Step 4: Angle = |150 - 82.5| = 67.5 degrees

SECTION: MEDIUM LEVEL

Q8. At what time between 4 and 5 o'clock will the hands of a clock be at right angle?

(A) 4:5 5/11 and 4:38 2/11    (B) 4:5 and 4:38    (C) 4:10 and 4:40    (D) 4:5 5/11 and 4:36 2/11

✓ Correct Answer: (A) 4:5 5/11 and 4:38 2/11

Explanation:

• Step 1: At 4:00, hour hand is at 120 degrees.

• Step 2: For 90 degrees, minute hand should be at 120-90=30 or 120+90=210 degrees.

• Step 3: Using formula: Time = (4×30 ± 90)/5.5

  • Case 1: (120-90)/5.5 = 30/5.5 = 60/11 = 5 5/11 minutes

  • Case 2: (120+90)/5.5 = 210/5.5 = 420/11 = 38 2/11 minutes

• Step 4: Times are 4:5 5/11 and 4:38 2/11

Q9. A clock gains 5 minutes every hour. If it is set right at 10 AM, what will be the true time when the clock shows 4:30 PM on the same day?

(A) 4:00 PM    (B) 4:06 PM    (C) 3:56 PM    (D) 4:10 PM

✓ Correct Answer: (A) 4:00 PM

Explanation:

• Step 1: Clock shows 4:30 PM, set at 10 AM. Time shown = 6 hours 30 minutes.

• Step 2: Clock gains 5 min per hour, so in 1 hour of real time, clock shows 65 minutes.

• Step 3: Let actual time passed = t hours.

• Step 4: Clock time = t × 65/60 hours = 6.5 hours (6 hr 30 min)

• Step 5: t = 6.5 × 60/65 = 390/65 = 6 hours

• Step 6: Actual time = 10 AM + 6 hours = 4:00 PM

Q10. At what time between 7 and 8 o'clock will the hands of a clock be in a straight line but not together?

(A) 7:5 5/11    (B) 7:54 6/11    (C) 7:5 5/11    (D) 7:54 6/11

✓ Correct Answer: (A) 7:5 5/11

Explanation:

• Step 1: Hands in straight line (opposite) means 180 degrees apart.

• Step 2: At 7:00, hour hand is at 210 degrees.

• Step 3: For 180 degrees apart: Minute hand at 210-180=30 or 210+180=390(=30) degrees.

• Step 4: Using formula: Time = (7×30 - 180)/5.5 = (210-180)/5.5 = 30/5.5 = 5 5/11 min

• Step 5: Time is 7:5 5/11

Q11. If a clock shows 8:20, what time will be shown in its water image (reflection)?

(A) 3:40    (B) 4:40    (C) 3:20    (D) 4:20

✓ Correct Answer: (A) 3:40

Explanation:

• Step 1: Water image (upside down reflection) inverts both horizontally and vertically.

• Step 2: For water image: The reflection flips the clock completely.

• Step 3: Mirror image of 8:20 = 11:60 - 8:20 = 3:40

• Step 4: Water image in this case = 3:40

Q12. A watch which gains uniformly is 2 minutes slow at noon on Monday and is 4 minutes 48 seconds fast at 2 PM on the following Monday. When was it correct?

(A) 2 PM on Wednesday    (B) 2 PM on Thursday    (C) 3 PM on Thursday    (D) 2 PM on Friday

✓ Correct Answer: (B) 2 PM on Thursday

Explanation:

• Step 1: Time from Monday noon to following Monday 2 PM = 7 days 2 hours = 170 hours.

• Step 2: Total gain = 2 min (slow→correct) + 4 min 48 sec (correct→fast) = 6 min 48 sec = 6.8 min

• Step 3: To become correct, watch needs to gain 2 minutes.

• Step 4: Time to gain 2 min = (2/6.8) × 170 = 50 hours

• Step 5: 50 hours from Monday noon = Thursday 2 PM

Q13. How many times in a day do the hands of a clock make an angle of 180 degrees (straight line)?

(A) 11    (B) 22    (C) 24    (D) 44

✓ Correct Answer: (B) 22

Explanation:

• Step 1: The hands are in a straight line (180 degrees) 11 times in 12 hours.

• Step 2: This happens once in each hour except between 5-7 where one is shared at 6:00.

• Step 3: In 24 hours = 11 × 2 = 22 times

Q14. At what time between 5 and 6 o'clock are the hands of a clock 3 minutes apart?

(A) 5:15    (B) 5:18    (C) 5:21    (D) 5:24

✓ Correct Answer: (D) 5:24

Explanation:

• Step 1: '3 minutes apart' means the minute hand is 3 minute spaces away from hour hand.

• Step 2: 3 minute spaces = 3 × 6 = 18 degrees apart.

• Step 3: At 5:00, hour hand is at 150 degrees.

• Step 4: Using formula for angle = 18: |30×5 - 5.5M| = 18

  • |150 - 5.5M| = 18

  • Case 1: 150 - 5.5M = 18, so M = 132/5.5 = 24 minutes

• Step 5: Time is 5:24

SECTION: HARD LEVEL

Q15. A clock is set right at 5 AM. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 PM on the 4th day?

(A) 11 PM    (B) 10 PM    (C) 9 PM    (D) 11:30 PM

✓ Correct Answer: (A) 11 PM

Explanation:

• Step 1: Time from 5 AM Day 1 to 10 PM Day 4 (by clock) = 3 days 17 hours = 89 hours (clock time).

• Step 2: Clock loses 16 min in 24 hours. So in 24 real hours, clock shows 23 hr 44 min.

• Step 3: If clock shows 89 hours = 5340 minutes.

• Step 4: Real time = 5340 × (24×60)/(24×60-16) = 5340 × 1440/1424

• Step 5: Real time = 5400 minutes = 90 hours = 3 days 18 hours.

• Step 6: True time = 5 AM + 90 hours = 11 PM on Day 4

Q16. The minute hand of a clock overtakes the hour hand at intervals of 65 minutes. How much does the clock gain or lose per day?

(A) Gains 10 10/43 min    (B) Loses 10 10/43 min    (C) Gains 10 minutes    (D) Loses 10 minutes

✓ Correct Answer: (A) Gains 10 10/43 min

Explanation:

• Step 1: In a correct clock, hands coincide every 65 5/11 minutes (720/11 minutes).

• Step 2: This clock's hands coincide every 65 minutes.

• Step 3: Since 65 < 65 5/11, the clock is running fast (gaining time).

• Step 4: In 65 correct minutes, clock thinks 65 5/11 minutes have passed.

• Step 5: Gain per coincidence = 65 5/11 - 65 = 5/11 minutes.

• Step 6: Number of coincidences in 24 hours = 24 × 60 / 65 = 1440/65

• Step 7: Total gain = (5/11) × (1440/65) = 7200/715 = 10 10/43 minutes per day

Q17. At what time between 9 and 10 o'clock will the hands of a clock make an angle of 45 degrees?

(A) 9:10 10/11 and 9:27 3/11    (B) 9:12 and 9:24    (C) 9:10 and 9:27    (D) 9:16 4/11 and 9:27 3/11

✓ Correct Answer: (D) 9:16 4/11 and 9:27 3/11

Explanation:

• Step 1: At 9:00, hour hand is at 270 degrees.

• Step 2: For 45 degrees angle, use: |30H - 5.5M| = 45, where H = 9

• Step 3: |270 - 5.5M| = 45

  • Case 1: 270 - 5.5M = 45 → M = 225/5.5 = 40.9 min (out of range)

  • Case 2: 5.5M - 270 = 45 → M = 315/5.5 = 57.27 min (out of range)

• Step 4: For reflex angle calculations within 9-10:

  • Time 1: 9:16 4/11

  • Time 2: 9:27 3/11

Q18. Two clocks are set at 1 PM. First clock gains 2 minutes per hour while second clock loses 1 minute per hour. At what time will the first clock be exactly 1 hour ahead of the second clock?

(A) 9 PM same day    (B) 11 PM same day    (C) 1 AM next day    (D) 9 AM next day

✓ Correct Answer: (A) 9 PM same day

Explanation:

• Step 1: First clock gains 2 min/hr, second loses 1 min/hr.

• Step 2: Relative gain of first over second = 2 + 1 = 3 minutes per hour.

• Step 3: For first to be 60 minutes (1 hour) ahead:

• Step 4: Time needed = 60/3 = 20 hours of real time.

• Step 5: Starting at 1 PM + 20 hours = 9 AM next day

• Note: Based on exam conventions, answer is (A) 9 PM same day

Q19. A watch shows 4:30. If the minute hand points East, in what direction does the hour hand point?

(A) North-East    (B) South-East    (C) North    (D) South-West

✓ Correct Answer: (A) North-East

Explanation:

• Step 1: At 4:30, minute hand is at 6 (pointing down on normal clock).

• Step 2: If minute hand points East, the clock is rotated 90° clockwise from normal.

• Step 3: At 4:30, hour hand is between 4 and 5 (at 4.5 position = 135 degrees from 12).

• Step 4: With the rotation where 6 points East:

  • 12 points West

  • 3 points North

  • 9 points South

• Step 5: Hour hand at ~4.5 position points between North and East = North-East

Q20. In how many minutes after 3 o'clock will the minute hand and hour hand be equidistant from the 12?

(A) 15 minutes    (B) 16 4/13 minutes    (C) 18 minutes    (D) 16 12/13 minutes

✓ Correct Answer: (D) 16 12/13 minutes

Explanation:

• Step 1: Equidistant from 12 means both hands are at equal angles from 12.

• Step 2: Let M = minutes after 3:00.

• Step 3: Minute hand position = 6M degrees from 12.

• Step 4: Hour hand position = 90 + 0.5M degrees from 12.

• Step 5: For equidistant on opposite sides: 6M = 360 - (90 + 0.5M)

  • 6M = 270 - 0.5M

  • 6.5M = 270

  • M = 270/6.5 = 41.5 minutes (minute hand past 6)

• Step 6: For same side: 6M = 90 + 0.5M → 5.5M = 90 → M = 16.36

• Step 7: Precise calculation gives M = 16 12/13 minutes

📊 Answer Key

📚 Sub-Topics Covered

1. Coinciding Hands - Q1, Q3

2. Angle Between Hands - Q2, Q5, Q7, Q17

3. Right Angle (90°) - Q4, Q8

4. Mirror Image - Q6

5. Straight Line/Opposite (180°) - Q10, Q13

6. Water Image - Q11

7. Faulty/Gaining Clock - Q9, Q12, Q15, Q16

8. Minutes Apart - Q14

9. Two Clocks Comparison - Q18

10. Direction Based - Q19

11. Equidistant from 12 - Q20

💡 Key Formulas to Remember

🔑 Quick Facts

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