Reasoning
Analogy Coding-Decoding Syllogism Blood Relations Direction & Distance Series Statement & Arguments Puzzles Calendar & Clock Non-Verbal Reasoning Cubes & Dice Venn Diagram
Module 2 · SSC CGL Reasoning

Calendar & Clock

Weekdays, angles, odd days, gain/loss.
Calendar · Clock Angles · Gain/Loss
🎯 Take Mock Test

Learning Objectives

  • Understand the fundamental concepts of Calendar & Clock
  • Apply key formulas and techniques to solve problems
  • Practice with exam-level questions to build speed and accuracy

Key Concepts

Introduction to Calendar & Clock

Calendar and Clock problems test your ability to calculate dates, weekdays, angles, and time-related phenomena. SSC CGL typically asks 1-2 questions from each sub-topic in Tier 1, and 2-3 in Tier 2. These are FORMULA-BASED and 100% predictable — master the formulas and you'll never get one wrong.

Part 1: Calendar — All Concepts

The Odd Days Concept (Foundation)

An ordinary year has 365 days = 52 weeks + 1 odd day. A leap year has 366 days = 52 weeks + 2 odd days. The weekday advances by the number of odd days modulo 7.

Leap Year Identification (2-Second Rule)

  • A year is a leap year if divisible by 4 (e.g., 2024, 2028).
  • Exception: Century years (ending in 00) must be divisible by 400 to be leap years.
  • 1900 → Not a leap year (divisible by 4 but not by 400).
  • 2000 → Leap year (divisible by 400).
  • 2100 → Not a leap year.

Month Code Method (Fastest Day Calculation)

Memorize month codes: JFM = 033, AMJ = 614, JAS = 624, OND = 035

  • January = 0, February = 3, March = 3
  • April = 6, May = 1, June = 4
  • July = 6, August = 2, September = 4
  • October = 0, November = 3, December = 5

For LEAP YEAR January: code = 0 (same). February: code = 6 (was 3, add 1 for leap year). Actually, only Jan and Feb change in leap year: Jan=0→0, Feb=3→6 (add 3+1=... wait, Feb has 29 days in leap year = 1 extra odd day. Feb code becomes Jan code + 31 mod 7 = 0+3=3? No, the month code for Feb in a normal year = 3. In leap year, the extra day shifts subsequent months: Jan=0 stays, Feb becomes 6 (since Jan has 31 days = 3 odd days, and Feb 29 = 1 odd day, so Feb starts 3+1=4 days after Jan start... this is getting complex. Just use the standard formula below.)

âš¡ Speed Trick #1: The Day Formula (Any Date)
Day = (Date + Month Code + Year Code + Century Code - Leap Year Adjustment) mod 7
0=Sunday, 1=Monday, ..., 6=Saturday
Month Codes: Jan=0, Feb=3, Mar=3, Apr=6, May=1, Jun=4, Jul=6, Aug=2, Sep=5, Oct=0, Nov=3, Dec=5
Year Code for 2000-2099: (YY + floor(YY/4)) mod 7, where YY = last 2 digits of year.
Century Codes: 1900s=0, 2000s=6 (or -1 mod 7), 2100s=4, 2200s=2
Leap Year Adjustment: Subtract 1 if Jan/Feb of LEAP year.
Example: 15 Aug 1947. Date=15, Month Code Aug=2, Year=47→Code=(47+11)=58→58 mod 7=2, Century 1900=0. No LEAP adj (Aug). Total = 15+2+2+0 = 19 → 19 mod 7 = 5 = Friday ✓

Same Calendar Years

A calendar repeats when the total odd days between years is a multiple of 7.

  • For a NORMAL year: add 6 years (or 11 years) to get same calendar.
  • For a LEAP year: add 28 years to get same calendar.
  • Examples: 2023 (normal) → 2023+6=2029 has same calendar. 2024 (leap) → 2024+28=2052 has same calendar.

SSC CGL Calendar Variants

Variant 1: Find Weekday
What day was 26 Jan 1950?
Date=26, Jan=0, Year=50→(50+12)=62→62 mod 7=6, Century 1900=0. Sum=26+0+6+0=32→32 mod 7=4 → Thursday. ⏱ 15 sec
Variant 2: Same Calendar
Which year has the same calendar as 2023?
2023 is normal year → add 6 → 2029. ⏱ 5 sec
Variant 3: Odd Days Count
How many odd days in 100 years?
100 years = 76 normal + 24 leap = 76×1 + 24×2 = 124 odd days. 124 mod 7 = 5 odd days. ⏱ 8 sec
Variant 4: Day on Given Date
If 15 Aug 1947 was Friday, what day was 15 Aug 1950?
1947→1948 (leap, odd=2), 1948→1949 (normal, odd=1), 1949→1950 (normal, odd=1). Total odd=4. Friday + 4 = Tuesday. ⏱ 12 sec
âš¡ Speed Trick #2: The Reference Date Method
Memorize: 1 Jan 2000 = Saturday. Then any date in 2000-2099 can be calculated using: Day = (Date + Month Code + (YY + floor(YY/4))) mod 7, where 0=Sat,1=Sun,2=Mon,... If Jan/Feb of leap year, subtract 1. This is the FASTEST method for current century dates.

Part 2: Clock — All Concepts

Essential Formulas (Memorize)

  • Minute hand speed = 360°/60 min = 6° per minute
  • Hour hand speed = 360°/12 hr = 30° per hour = 0.5° per minute
  • Relative speed = 6° - 0.5° = 5.5° per minute
  • Angle between hands at H hours and M minutes: |30H - 5.5M|° or use |30H - 11M/2|°
  • Hands coincide when: M = 60H/11 (in minutes past H o'clock)
  • Hands are opposite (180°) when: 30H - 5.5M = 180 or -180 → M = (30H ± 180)/5.5
  • Mirror image time: Subtract from 11:60 (or 23:60 for 24-hr format)

SSC CGL Clock Variants

Variant 1: Angle Between Hands
What is the angle between hands at 3:30?
H=3, M=30. Angle = |30×3 - 5.5×30| = |90 - 165| = 75°. ⏱ 8 sec
Variant 2: Time When Hands Coincide
Between 4 and 5, when do the hands coincide?
M = 60H/11 = 60×4/11 = 240/11 = 21 9/11 min past 4. Time = 4:21:49. ⏱ 5 sec
Variant 3: Mirror Image
If a clock shows 4:45, what time does its mirror image show?
11:60 - 4:45 = 7:15. ⏱ 5 sec
Variant 4: Gain/Loss
A clock gains 5 min per day. What time will it show at 6 PM when actual time is 6 PM after 3 days?
Gain per day = 5 min. In 3 days = 15 min gain. At 6 PM actual, clock shows 6:15 PM. ⏱ 5 sec
Variant 5: Hands Opposite
Between 5 and 6, when are the hands opposite (180°)?
30H - 5.5M = 180. 30×5 - 5.5M = 180 → 150 - 5.5M = 180 → -5.5M = 30 → M = -30/5.5 = -5.45 (not valid). So use 5.5M - 30H = 180: 5.5M - 150 = 180 → 5.5M = 330 → M = 60. At 5:60 = 6:00, hands are opposite? At 6:00, angle = |30×6 - 5.5×0| = 180° ✓. So at 6:00 sharp. ⏱ 10 sec
Variant 6: Right Angle (90°)
Between 3 and 4, at what time are the hands at right angle?
Two solutions: (1) 30H - 5.5M = 90 → 90 - 5.5M = 90 → M = 0. At 3:00 sharp. (2) 5.5M - 30H = 90 → 5.5M - 90 = 90 → 5.5M = 180 → M = 32.727 = 32 8/11. So at 3:00 and 3:32:44. ⏱ 12 sec
âš¡ Speed Trick #3: The Angle Shortcut
For finding angle at H:M, just use: Angle = |30H - 5.5M|°. If answer > 180°, subtract from 360° (we take the smaller angle). Example: 8:30 → |240 - 165| = 75°. At 8:00 → |240 - 0| = 240 → smaller angle = 360-240 = 120°. ⏱ 5 sec
âš¡ Speed Trick #4: Mirror Image Formula
Mirror time = 11:60 - actual time (for 12-hr clock). For 24-hr: 23:60 - actual time. Example: 8:25 → 11:60 - 8:25 = 3:35. Check: Mirror of 8:25 should be 3:35 (since 8:25 and 3:35 are symmetric about 12:00). ⏱ 3 sec

Common Mistakes (15 Mistakes)

  • Mistake 1: Forgetting century year exception (1900 not leap, 2000 is).
  • Mistake 2: Using wrong month code — memorize JFM=033, AMJ=614, JAS=624, OND=035.
  • Mistake 3: Forgetting to subtract 1 for Jan/Feb of leap year.
  • Mistake 4: Confusing AM/PM in clock problems.
  • Mistake 5: Using 12-hour format for mirror images when should use 24-hour.
  • Mistake 6: Not converting hours to minutes properly in angle formula.
  • Mistake 7: Forgetting that the smaller angle is asked (if >180, subtract from 360).
  • Mistake 8: Misidentifying leap year (2024 is, 2100 is not).
  • Mistake 9: Counting odd days incorrectly (forgetting leap years in the range).
  • Mistake 10: Not including the current year in odd day count.
  • Mistake 11: Confusing '0 odd days = Sunday' with '0 odd days = Monday'.
  • Mistake 12: Forgetting the clock gain/loss accumulates over days.
  • Mistake 13: Using wrong formula for coinciding time (M=60H/11, not 12H/11).
  • Mistake 14: Not handling the two possible right-angle positions (hands 90° ahead and 90° behind).
  • Mistake 15: Spending >30 seconds on a calendar/clock question — the formulas give instant answers.

Pro Tips from Toppers

🏆 Topper Secret
Calendar and Clock are the MOST FORMULAIC topics in SSC CGL Reasoning. There are only 6-7 question types and each has a direct formula. If you memorize:
1. Month codes (JFM=033, AMJ=614, JAS=624, OND=035)
2. Angle formula (|30H-5.5M|)
3. Coinciding formula (M=60H/11)
4. Mirror formula (11:60 - actual)
You'll never get a question wrong from this topic. Practice each formula 5 times — total prep time: 30 minutes for lifetime mastery.

Practice Questions