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Clock & Calendar Logic

General Intelligence & Reasoning · SSC Reasoning Mixed Advanced

Useful for: SSC CGL

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Overview

Clock questions use the angle formula and hand speeds; calendar questions count odd days.

Key points

Angle between the hands at H:M = |30H − 5.5M|; if over 180°, subtract from 360°.
The minute hand gains 5.5° per minute over the hour hand.
Hands coincide 11 times in 12 hours (22 in a day) and are at right angles 22 times in 12 hours (44 in a day).
Odd days: an ordinary year has 1 odd day, a leap year 2.
Century odd days: 100 years = 5, 200 = 3, 300 = 1, 400 = 0.

Explanation

A leap year is divisible by 4; century years must be divisible by 400 (2000 is leap, 1900 is not).
Days after today: take the number of days mod 7.
The calendar of a year repeats after 6, 11 or 28 years depending on leap years.
Mirror image of a clock: subtract the time from 11:60.

Step by step

Choose clock or calendar method.
Apply the formula or odd-day count.
Check the reasonable range.

Examples

Angle at 3:40 = |90 − 220| = 130°.
If today is Monday, the day after 61 days is Saturday (61 mod 7 = 5).
If 1 January 2023 was a Sunday, 1 January 2024 was a Monday (2023 has 1 odd day).

Traps and advanced points

Trap: Forgetting to take 360° − θ when θ exceeds 180°.
Trap: Treating 1900 as a leap year.
Trap: Counting the starting day itself.

Quick revision

θ = |30H − 5.5M|.
Ordinary year 1 odd day, leap 2.
400 years = 0 odd days.

Practice MCQs

Which century year is a leap year?
1. 1900
2. 2100
3. 2200
4. 2000
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Answer: (d) 2000. Century year leap tab hota hai jab 400 se divisible ho; 2000 divisible by 400 hai.
What is the smaller angle between the clock hands at 8:28?
1. 86°
2. 116°
3. 71°
4. 101°
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Answer: (a) 86°. |30×8−5.5×28|=86°; smaller angle=86°.
What is the smaller angle between the clock hands at 1:07?
1. 10.62°
2. 23.5°
3. 38.5°
4. 8.5°
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Answer: (d) 8.5°. |30×1−5.5×7|=8.5°; smaller angle=8.5°.
What is the smaller angle between the clock hands at 1:21?
1. 70.5°
2. 100.5°
3. 115.5°
4. 85.5°
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Answer: (d) 85.5°. |30×1−5.5×21|=85.5°; smaller angle=85.5°.
What is the smaller angle between the clock hands at 1:35?
1. 192.5°
2. 177.5°
3. 162.5°
4. 147.5°
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Answer: (c) 162.5°. |30×1−5.5×35|=162.5°; smaller angle=162.5°.
What is the smaller angle between the clock hands at 1:42?
1. 159°
2. 144°
3. 174°
4. 189°
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Answer: (a) 159°. |30×1−5.5×42|=201°; smaller angle=159°.
What is the smaller angle between the clock hands at 1:49?
1. 120.5°
2. 105.5°
3. 150.5°
4. 135.5°
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Answer: (a) 120.5°. |30×1−5.5×49|=239.5°; smaller angle=120.5°.
What is the smaller angle between the clock hands at 1:56?
1. 67°
2. 112°
3. 82°
4. 97°
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Answer: (c) 82°. |30×1−5.5×56|=278°; smaller angle=82°.
What is the smaller angle between the clock hands at 2:03?
1. 43.5°
2. 28.5°
3. 58.5°
4. 73.5°
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Answer: (a) 43.5°. |30×2−5.5×3|=43.5°; smaller angle=43.5°.
What is the smaller angle between the clock hands at 2:10?
1. 20°
2. 35°
3. 6.25°
4. 5°
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Answer: (d) 5°. |30×2−5.5×10|=5°; smaller angle=5°.