Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।
Formulaसूत्र✓ Checked on 11 cases✓ 11 मामलों पर जाँची गई
The hands overlap every 65 5/11 minutes
Use it when:कब इस्तेमाल करें: “When between 4 and 5 o’clock are the hands together?”
Between H and H + 1 o’clock, the hands meet at 60H/11 minutes past H.
Right angles come 180/11 ≈ 16.36 minutes before and after each overlap.
Exampleउदाहरण
Between 4 and 5
→ 240/11 = 21 9/11 minutes past 4
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: The minute hand gains 5.5° a minute and must make up 30H degrees: 30H / 5.5 = 60H/11.
Limits:सीमाएँ: Between 11 and 12 the overlap is at 12:00 itself, so there are 11 overlaps in 12 hours, not 12.
Mental mathsमानसिक गणित✓ Checked on 103 cases✓ 103 मामलों पर जाँची गई
Mirror time = 11:60 − time
Use it when:कब इस्तेमाल करें: “A clock shows 3:25. What does its mirror image show?”
Subtract the time from 11:60 (that is, from 12:00).
If the time is after 11:00, subtract from 23:60 instead.
Exampleउदाहरण
Mirror image of 3:25
→ 11:60 − 3:25 = 8:35
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: A vertical mirror reflects every angle θ (measured from 12) to 360° − θ; for both hands that is the same as the time 12:00 − t.
Limits:सीमाएँ: For a mirror placed on the side only. Water (upside-down) images need a different rule, which is not covered here.
Solved examplesहल किए गए उदाहरण
Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।
Example 1उदाहरण 1 · Clock: angle between the hands · Easyआसान
What is the smaller angle (in degrees) between the hour hand and the minute hand of a clock at 9:00?
70 degrees
90 degrees
100 degrees
110 degrees
Answer:उत्तर:90 degrees
|30 × 9 − 5.5 × 0| = |270 − 0| = 270°.
More than 180°, so smaller angle = 360 − 270 = 90°.
Example 2उदाहरण 2 · Clock: angle between the hands · Mediumमध्यम
What is the smaller angle (in degrees) between the hour hand and the minute hand of a clock at 10:45?
39.5 degrees
52.5 degrees
58 degrees
63 degrees
Answer:उत्तर:52.5 degrees
|30 × 10 − 5.5 × 45| = |300 − 247.5| = 52.5°.
Smaller angle = 52.5°.
Example 3उदाहरण 3 · Clock: angle between the hands · Hardकठिन
What is the smaller angle (in degrees) between the hour hand and the minute hand of a clock at 4:33?
46 degrees
55.5 degrees
61.5 degrees
67.5 degrees
Answer:उत्तर:61.5 degrees
|30 × 4 − 5.5 × 33| = |120 − 181.5| = 61.5°.
Smaller angle = 61.5°.
Example 4उदाहरण 4 · Clock: angle between the hands · Mediumमध्यम
What is the smaller angle (in degrees) between the hour hand and the minute hand of a clock at 3:25?
43 degrees
47.5 degrees
52.5 degrees
59.5 degrees
Answer:उत्तर:47.5 degrees
|30 × 3 − 5.5 × 25| = |90 − 137.5| = 47.5°.
Smaller angle = 47.5°.
Example 5उदाहरण 5 · Clock: angle between the hands · Mediumमध्यम
What is the smaller angle (in degrees) between the hour hand and the minute hand of a clock at 9:55?
24.5 degrees
29.5 degrees
32.5 degrees
36 degrees
Answer:उत्तर:32.5 degrees
|30 × 9 − 5.5 × 55| = |270 − 302.5| = 32.5°.
Smaller angle = 32.5°.
Example 6उदाहरण 6 · Clock: angle between the hands · Mediumमध्यम
What is the smaller angle (in degrees) between the hour hand and the minute hand of a clock at 8:15?
142 degrees
157.5 degrees
173.5 degrees
197 degrees
Answer:उत्तर:157.5 degrees
|30 × 8 − 5.5 × 15| = |240 − 82.5| = 157.5°.
Smaller angle = 157.5°.
Common mistakesआम गलतियाँ
Keeping the hour hand fixed on the hour mark.
Giving the reflex angle when the question asks for the smaller one.
Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न
What is the formula for the angle between clock hands?
|30H − 5.5M| degrees, and 360 minus that if it exceeds 180.
How often do the hands overlap?
11 times in 12 hours, roughly every 65 5/11 minutes.