Clock & Calendar Reasoning: Formulas & Tricks

Clock and Calendar look intimidating but run on two or three formulas. Learn them once and these become guaranteed marks. CLOCK BASICS • A clock is 360°; each hour mark is 30° apart (360 ÷ 12). • The minute hand moves 6° per minute; the hour hand moves 0.5° per minute. • Angle between hands = |(30 × H) − (5.5 × M)|. If the answer exceeds 180°, subtract from 360°. • The hands coincide (0°) 11 times in 12 hours; they are opposite (180°) 11 times in 12 hours. CLOCK EXAMPLE Angle between the hands at 3:40? = |(30 × 3) − (5.5 × 40)| = |90 − 220| = 130°. CALENDAR: THE ODD-DAYS METHOD • "Odd days" = days left over after counting complete weeks. We map remainders 0–6 to days. • An ordinary year has 365 days = 52 weeks + 1 odd day. A leap year has 2 odd days. • Leap year rule: divisible by 4, BUT century years only if divisible by 400. So 2000 is leap, 1900 is not. • Day codes (taking Sunday = 0): 0-Sun, 1-Mon, 2-Tue, 3-Wed, 4-Thu, 5-Fri, 6-Sat. CALENDAR EXAMPLE What day was 15 August 1947 if 1 January 1947 was a Wednesday? Count days from 1 Jan to 15 Aug 1947 = 226 days. 226 ÷ 7 leaves remainder 2. Wednesday + 2 = Friday. So 15 August 1947 was a Friday (which it was). A USEFUL SHORTCUT The same calendar repeats after 11, 6 or 11 years for ordinary patterns, and exactly after 28 years in most cases — handy for "which future year has the same calendar" questions. Lock these formulas in with practice sets on Govt Exam Center.