RRB Group D · Bite-size lessons

Calendar and Clock

About 7 min · Mathematics · English

Time worked out from the lesson's 528 words at 150 words a minute, plus a minute for each question.

Calendar and Clock is a topic in Railway Group D that tests your logical thinking and numerical accuracy. Questions are straightforward and can be solved quickly once you master the formula and concept of odd days for calendar problems, and angle formulas for clock problems.

Key ideas

• Odd days are the extra days beyond complete weeks when calculating total days. One week = 0 odd days; 8 days = 1 odd day; 9 days = 2 odd days, and so on. To find the day of the week, calculate total odd days and apply modulo 7.
• Ordinary year has 365 days = 52 weeks + 1 day = 1 odd day. Leap year has 366 days = 52 weeks + 2 days = 2 odd days. A year is a leap year if divisible by 4, except century years (1800, 1900) which must be divisible by 400 (so 2000 was a leap year, but 1900 was not).
• Counting centuries: Every 100 years gives 76 ordinary years (1 odd day each = 76) + 24 leap years (2 odd days each = 48) = 124 odd days = 17 weeks + 5 odd days. So 100 years = 5 odd days; 200 years = 3 odd days; 300 years = 1 odd day; 400 years = 0 odd days.
• Month odd days (non-leap year): Jan=3, Feb=0, Mar=3, Apr=2, May=3, Jun=2, Jul=3, Aug=3, Sep=2, Oct=3, Nov=2, Dec=3. For leap years, add 1 to February (Feb=1) and adjust accordingly for dates after February.
• Clock angle formula: The angle between hour and minute hands at time H hours and M minutes is |30H - 6M + M/2| or |11M/2 - 30H|. Use the absolute value and if the result exceeds 180°, subtract from 360° to get the smaller angle.

Watch out for

• Forgetting leap-year adjustment: Students often forget to add +1 odd day to February in a leap year when calculating odd days for dates after February. Fix: Always check divisibility by 4 (and 400 for century years) first and adjust month odd days.
• Using 12-hour format incorrectly: When the problem states "3:30 PM," students use H=15 in the formula. Fix: Always convert to 12-hour format (3:30 PM → H=3), because clock formulas assume 12-hour cycles.
• Taking reflex angle instead of the smaller angle: After calculating the angle, if it's greater than 180°, students report it directly. Fix: Subtract from 360° to get the smaller angle unless the question specifically asks for the reflex angle.

Quick reference

• Ordinary year = 1 odd day; Leap year = 2 odd days; 100 years = 5 odd days.
• Angle formula: |(11M/2) - 30H|; if >180°, use 360° - angle.
• Hands coincide 11 times in 12 hours, at H×(60/11) minutes past each hour.
• Month odd days (non-leap): J=3, F=0, M=3, A=2, M=3, J=2, J=3, A=3, S=2, O=3, N=2, D=3.
• Day codes: 0=Sun, 1=Mon, 2=Tue, 3=Wed, 4=Thu, 5=Fri, 6=Sat.

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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