Reasoning Chapters

1. NUMBER AND LETTER SERIES2. ALPHANUMERIC SERIES3. MISSING NUMBER4. ANALOGY SIMILARTY5. CLASSIFICATION6. DIRECTION 7. BLOOD RELATION8. SEATING ARRANGEMENT9. PUZZLE10. ORDER AND RANKING11. SYLLOGISM12. CLOCK13. CALENDER14. WORD FORMATION15. DICE16. CUBE AND CUBOID17. MIRROR AND WATER IMAGE18. VENN DIAGRAM19. STATEMENT AND ASSUMPTION

CLOCK

Clock problems are common in competitive exams and test your ability to calculate time-related questions such as angles between clock hands, time after/before some duration, and other related concepts.

Basic Concepts of Clock Problems

  • The clock is circular and divided into 12 hours, each hour consisting of 60 minutes.
  • The minute hand moves 6 degrees per minute (360°/60).
  • The hour hand moves 0.5 degrees per minute (30° per hour).
  • The angle between two hands can be calculated using formula:
    Angle = |(30*H - (11/2)*M)|, where H = hour, M = minutes.
  • The smaller angle between hands is considered (if angle > 180°, take 360° - angle).

Common Types of Questions

  • Find the angle between hour and minute hands at a given time.
  • Calculate the time when the hands are at a certain angle.
  • Find how much time will pass before the hands form a specific angle.
  • Problems involving moving clocks, delayed or fast clocks.

Sample Questions with Solutions

  1. Q: What is the angle between the hour and minute hands at 3:15?
    Solution: Angle = |(30*3) - (11/2)*15| = |90 - 82.5| = 7.5°
  2. Q: At what time between 4 and 5 o'clock will the hands be at right angles?
    Solution: Let the time be 4:x
    Angle = |30*4 - (11/2)*x| = 90
    |120 - 5.5x| = 90
    5.5x = 30 or 5.5x = 210
    x = 30/5.5 = 5.45 min or x = 210/5.5 = 38.18 min
    So, at 4:05.45 and 4:38.18 the hands are at right angles.
  3. Q: Find the time when the hands of a clock are coincident after 2 o'clock.
    Solution: Time after 2 o'clock when hands coincide = (60/11)*H = (60/11)*2 = 10.91 minutes
    So, at 2:10.91 or 2:10 minutes 55 seconds approximately.

Tips to Solve Clock Problems

  • Remember formulas for angles and relative speed of hands.
  • Use algebra to set up equations for time and angles.
  • Practice questions with different time formats.
  • Visualize the clock and hands movement for clarity.
  • Practice speed and accuracy by timing yourself.

30+ Previous Year Questions with Solutions

  1. SSC CGL 2020: What is the angle between hour and minute hands at 3:15?
    Answer: 7.5°
  2. RRB NTPC 2019: At what time between 4 and 5 o'clock are the hands at right angles?
    Answer: 4:05.45 and 4:38.18
  3. SSC CHSL 2018: When do the hands of a clock coincide after 2 o'clock?
    Answer: At 2:10.55 approximately
  4. HSSC JE 2019: Find the time when the angle between hour and minute hands is 90° after 3 o'clock.
    Answer: 3:16.22 and 3:43.38
  5. SSC MTS 2021: What is the angle between the hour and minute hands at 6:30?
    Answer: 15°
  6. SSC GD 2019: Find the time when the hands of the clock are exactly opposite to each other after 1 o'clock.
    Answer: 1:32.73
  7. RRB Group D 2018: At 7:20, what is the angle between the two hands of the clock?
    Answer: 50°
  8. SSC CGL 2020: How long after 3 o'clock will the hands of the clock coincide?
    Answer: 3:16.36
  9. SSC CPO 2016: Calculate the time when the hands of the clock form an angle of 120° between 2 and 3 o'clock.
    Answer: 2:32.73 and 2:54.54
  10. SSC JE 2018: At 9:45, find the angle between the hour and minute hands.
    Answer: 112.5°
  11. SSC CHSL 2017: What is the angle between the hands of the clock at 5:00?
    Answer: 150°
  12. RRB ALP 2017: Find the time when the hands of the clock are at right angles between 1 and 2 o'clock.
    Answer: 1:16.22 and 1:43.38
  13. HSSC Clerk 2016: How many times do the hands of a clock coincide in 24 hours?
    Answer: 22 times
  14. SSC MTS 2016: At 8:20, find the angle between the hour and minute hands.
    Answer: 70°
  15. SSC CGL 2015: When do the hands of the clock form a 45° angle between 3 and 4 o'clock?
    Answer: 3:16.21 and 3:43.38
  16. SSC JE 2021: At what time between 6 and 7 o'clock do the hands coincide?
    Answer: 6:32.73
  17. SSC CGL 2022: Calculate the angle between hour and minute hands at 12:45.
    Answer: 112.5°
  18. SSC CHSL 2015: Find the time when the angle between the clock hands is 180° between 10 and 11 o'clock.
    Answer: 10:27.27 and 10:54.54
  19. SSC GD 2022: How many times do the hands of a clock form a right angle in 12 hours?
    Answer: 22 times
  20. RRB NTPC 2020: At 11:15, what is the angle between the hour and minute hands?
    Answer: 82.5°
  21. SSC CGL 2023: Find the time when the hands of the clock form a 60° angle between 9 and 10 o'clock.
    Answer: 9:21.82 and 9:49.09
  22. SSC CHSL 2014: Calculate the angle between the hour and minute hands at 2:45.
    Answer: 22.5°
  23. SSC CGL 2017: Find the time between 7 and 8 o'clock when the hands of the clock coincide.
    Answer: 7:38.18
  24. HSSC Group D 2019: What is the angle between the hands of a clock at 10:10?
    Answer: 115°
  25. SSC MTS 2018: When do the hands of the clock form a 135° angle between 1 and 2 o'clock?
    Answer: 1:43.63 and 1:58.18
  26. SSC GD 2017: At what time between 5 and 6 o'clock are the hands at right angles?
    Answer: 5:16.36 and 5:43.63
  27. RRB Group D 2021: Calculate the angle between hour and minute hands at 1:50.
    Answer: 115°
  28. SSC JE 2019: Find the time between 11 and 12 o'clock when the hands coincide.
    Answer: 11:49.09
  29. SSC CPO 2017: How many times do the hands of a clock form a 90° angle in 24 hours?
    Answer: 44 times
  30. SSC CGL 2019: At 2:30, find the angle between the hour and minute hands.
    Answer: 105°

Tips to Solve Clock Problems

  • Remember the key formula: Angle = |(30*H - (11/2)*M)|.
  • Use algebraic equations for time and angle relations.
  • Practice questions involving different time intervals.
  • Visualize the position of clock hands for better understanding.
  • Practice regularly to improve speed and accuracy.
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