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SSC CGL Reasoning · Calendar and Clock

Calendar

The days of the week repeat every 7 days, so only the remainder after dividing a number of days by 7 (the odd days) moves the weekday; a year adds 1 odd day, a leap year 2.

All Calendar and Clock notes

Why this matters

Nine questions in the bank, five from the 2023 shifts and four from the 2025 shifts, seven EASY and two MODERATE. Three count dates forward or back, three find the weekday after a number of days, and three use the odd days in a year or the leap-year rule. None of the nine is about a clock.

Concept 1 of 3: Counting dates forward and back

Inside one month, moving a date is plain adding and taking away. The only care needed is at the end of a month, where you must know how many days that month has.

Definition

  • n days after a date in the same month is date +n+ n; n days before is date −n- n.
  • "How many days after A was B?" is B's date minus A's date. Do not count both ends.
  • Crossing a month end: take away the month's length. For example, 6 days after 28 April is 34 April, which is 4 May.
  • Month lengths: 31 days for January, March, May, July, August, October and December; 30 for April, June, September and November; February has 28, or 29 in a leap year.
  • A chain of events: fix the date of the event you are given first, then move from it to each of the others one at a time.

Worked example

A fair opens in Pune 9 days after one in Nagpur. A fair in Nashik opens 5 days before the Pune fair. The Nagpur fair opens on 4 March. When does the Nashik fair open?
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 24 Sep 2025, Shift 1 · Q2Easy

Example 1 · Calendar and Clock · Calendar

The seminar in Ranchi happened 3 days before Patna. The seminar in Bhubaneswar happened 2 days after Patna. If Ranchi's seminar was on 11th11^{th} August, when was Bhubaneswar's?

Counting both ends

"How many days after the 12th is the 20th?" is 20−12=820 - 12 = 8. Counting both the 12th and the 20th gives 9, which is the number of days from the first to the last inclusive, a different question.

Giving every month 30 days

Crossing the end of a month, use that month's real length. Three days after 30 January is 2 February, but three days after 30 April is 3 May.
Drill 2 more on counting dates forward and back

Concept 2 of 3: The weekday after a number of days

Every 7 days the week comes back to the same day, so whole weeks can be thrown away. Only the days left over, the odd days, move you along the week.

Definition

  • Odd days: divide the number of days by 7 and keep the remainder.
  • Forward: move the weekday on by the odd days. Backward (days ago, or the day before): move it back.
  • Same weekday: dates 7, 14, 21 or 28 days apart fall on the same weekday. If the 3rd is a Sunday, so are the 10th, 17th, 24th and 31st.
  • Across months: count the days left in the first month, then the days into the next.
  • Fast route: jump by 7s to the nearest date that has the weekday you know, then count the last few days by hand.

Odd days

Odd days=remainder when the number of days is divided by 7\text{Odd days} = \text{remainder when the number of days is divided by } 7

Worked example

Today is Wednesday. What day of the week will it be after 100 days?
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 19 Sep 2025, Shift 2 · Q24Easy

Example 2 · Calendar and Clock · Calendar

If the 7th day of a month is three days earlier than Friday, What day will it be on the 20th day of the month?

Counting today as one of the days

One day after Monday is Tuesday. The starting day is day 0, so after 7 days you are back on Monday, not on Sunday.

Forgetting the month's length

To move from a date in one month to a date in the next, you need the days left in the first month, and that depends on whether it has 28, 29, 30 or 31 days.
Drill 2 more on the weekday after a number of days

Concept 3 of 3: Odd days in a year and leap years

A year is 52 whole weeks and one day more, so the same date next year falls one weekday later. A leap year has one more day again, so it moves the date two weekdays.

Definition

  • An ordinary year: 365 days =52= 52 weeks +1+ 1 odd day. A leap year: 366 days == 2 odd days.
  • Same date a year later: the weekday moves on by 1, or by 2 if a 29 February falls inside that year's span.
  • Leap-year rule: a year divisible by 4 is a leap year. A century year (ending in 00) must be divisible by 400: 2000 was a leap year, 1900 was not.
  • Divisible by 4: look only at the last two digits. 1996 is a leap year because 96 is a multiple of 4.
  • Over several years: add 1 odd day for every year, plus 1 more for every 29 February in between, then take the remainder on division by 7.

Odd days over whole years

Odd days=number of years+number of 29 Februarys in between\text{Odd days} = \text{number of years} + \text{number of 29 Februarys in between}

Worked example

15 August 2019 was a Thursday. What day of the week was 15 August 2021?
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2023 · Tier I, 25 Jul 2023, Shift 3 · Q11Moderate

Example 3 · Calendar and Clock · Calendar

If 31 January 2009 was a Saturday, then what was the day of the week on 30 January 2013?

Calling every century year a leap year

1900 is divisible by 4 but not by 400, so it was not a leap year. Only century years such as 1600 and 2000 are.

Giving the extra day to the wrong span

The leap day counts only if 29 February lies inside the span. 1 March 2023 to 1 March 2024 contains it; 1 March 2024 to 1 March 2025 does not, although 2024 is a leap year.
Drill 2 more on odd days in a year and leap years

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

  • The weekday after a number of days

    Odd days

    Odd days=remainder when the number of days is divided by 7\text{Odd days} = \text{remainder when the number of days is divided by } 7
  • Odd days in a year and leap years

    Odd days over whole years

    Odd days=number of years+number of 29 Februarys in between\text{Odd days} = \text{number of years} + \text{number of 29 Februarys in between}

Watch out for (6)

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