Calendar & Clock — Study Notes

Overview

Calendar and Clock questions are staples in the Logic & Reasoning section of UPSSSC PET. Typically, you'll encounter 2–3 questions testing your ability to calculate the day of the week for a given date, understand the concept of odd days, compute the angle between hour and minute hands, and solve clock-mirror problems. These questions are largely formula-driven and mechanical—master the formulas and practice calculation speed to score full marks.

The Calendar segment relies on understanding leap years, odd days, and day-counting methods. The Clock segment tests angle calculation using simple formulas and mirror/water-image logic. Both are high-scoring because they require minimal reasoning once you know the method. Students who memorise the key rules and practice 15–20 problems can confidently attempt every question in this sub-topic on exam day.

Focus on quick mental math, especially divisions and multiplications involving 7, 30, and 360, since these constants appear repeatedly in both calendar and clock problems.

Key Concepts

• **Odd Days:** The remainder when total days are divided by 7. Each week has 7 days; the "odd" days determine the shift in the day of the week. For example, 15 days = 2 weeks + 1 odd day.
• **Leap Year:** A year divisible by 4 is a leap year (366 days = 52 weeks + 2 odd days), except century years which must be divisible by 400. Non-leap years have 365 days = 52 weeks + 1 odd day.
• **Day Calculation:** Assign codes 0=Sunday, 1=Monday, …, 6=Saturday. Add odd days from the reference date, divide total by 7, and use the remainder to find the day.
• **Clock Angles:** The minute hand moves 6° per minute (360°/60 min). The hour hand moves 0.5° per minute (30°/60 min). Angle between hands = |11m/2 - 30h| where h = hour, m = minute past the hour. If the result exceeds 180°, subtract from 360° to get the acute angle.
• **Mirror Image of Clock:** In a plane mirror, the clock appears reversed. The mirror time formula: Mirror time = 12:00 - Actual time (for hours ≤ 12). Adjust minutes as 60 - actual minutes and hours as 11 - actual hours (with carry-over).
• **Right-Angle/Straight-Line Problems:** Hands coincide 11 times in 12 hours, form right angles 22 times, and form straight lines 11 times. Use these frequencies for time-interval questions.

Formulas / Key Facts

1. **Odd days in a year:** Ordinary year = 1 odd day; Leap year = 2 odd days. 2. **Odd days in a century:** 100 years = 76 ordinary + 24 leap = 76×1 + 24×2 = 124 odd days = 124 mod 7 = 5 odd days. 3. **Odd days in 400 years:** 400 years = 0 odd days (exact multiple of weeks). Use this to simplify large-year calculations. 4. **Day code:** Sunday=0, Monday=1, Tuesday=2, Wednesday=3, Thursday=4, Friday=5, Saturday=6. 5. **Month codes (for day calculation):** Jan=0, Feb=3, Mar=3, Apr=6, May=1, Jun=4, Jul=6, Aug=2, Sep=5, Oct=0, Nov=3, Dec=5 (for non-leap year; for leap year Jan=6, Feb=2, rest same). 6. **Angle between clock hands:** θ = |11m/2 - 30h| degrees. If θ > 180°, take 360° - θ. 7. **Mirror time formula:** Mirror hour = 11 - actual hour; Mirror minute = 60 - actual minute. Adjust if minutes = 0. 8. **Coinciding hands in 12 hours:** 11 times (0:00, ~1:05, ~2:11, …, not at 11:00). 9. **Hands at 90° in 12 hours:** 22 times; Hands at 180° in 12 hours:** 11 times. 10. **Time gap between consecutive coincidences:** 12/11 hours = 65 5/11 minutes.