Opposite Clock Hands with Angle and Timing Examples
Opposite Clock Hands questions ask when the hour hand and minute hand are separated by 180°. The solution uses their angular positions and relative movement. This page covers the opposite clock hands formula, the method for finding the exact time, fractional minutes, seconds conversion and solved aptitude examples.
On this page
What Are Opposite Clock Hands?
At H hours and M minutes, the hour hand is at 30H + 0.5M degrees and the minute hand is at 6M degrees. Therefore, their directed angular difference is 30H − 5.5M degrees. For opposite hands, this difference must be 180° modulo 360°. In a 12-hour period, the hands are opposite 11 times.
Opposite Clock Hands Video Lessons
Watch short topic-wise lessons for quick revision.
Clock Coincidence, Right Angle and Opposite Times
Learn how to determine clock times when the hour and minute hands coincide, form a right angle, or lie in opposite positions.
Opposite Clock Hands Formula & Tricks
Important Formulas
H is the hour shown on the clock and M is the number of minutes after that hour.
The hands are opposite when their angular separation is a straight angle.
Use the value of the sign that gives 0 ≤ M < 60. This gives the minute value when the hands are opposite during the Hth hour.
The minute hand gains on the hour hand at 5.5° per minute. A further opposite position repeats after 720/11 minutes, or 65 5/11 minutes.
Quick Tricks
For opposite-hand questions, the minute value usually has denominator 11. Apply M = (60H ± 360)/11 and retain the answer between 0 and 60.
Multiply the fractional part of a minute by 60 to obtain seconds.
A result of 49 minutes belongs to the interval from 3 to 4 when H = 3. Reject any calculated minute value below 0 or at least 60.
Opposite Clock Hands Concepts
Finding the Opposite Time in a Given Hour
The hour hand moves continuously, so its position includes 0.5M degrees. For example, between 3 and 4, use M = (60 × 3 + 360)/11 = 540/11 = 49 1/11 minutes. The exact time is 3:49 1/11, or approximately 3:49:05.
Using Angular Positions Directly
At H:M, the minute-hand angle is 6M and the hour-hand angle is 30H + 0.5M. Hence, 6M − (30H + 0.5M) = 180° can be solved for M when the minute hand is ahead by 180°. If the hour hand is ahead, use the corresponding negative or modulo-360° equation.
Exact Opposite Position at 6:00
At 6:00, the angular difference is 30 × 6 − 0 = 180°. This is the only whole-hour opposite position on a standard 12-hour clock.
Number of Opposite Positions
The relative angular speed is 5.5° per minute. Consecutive opposite positions are separated by 360/5.5 = 720/11 minutes, which is 65 5/11 minutes. Over 12 hours, this produces 11 opposite positions.
Opposite Clock Hands Visual Guide
Use the diagram or chart below to understand the concept clearly.
Clock Hands Opposite Between 3 and 4
Learn more concepts on PrepShots
Start ₹1 Trial →Practice Opposite Clock Hands Questions
Practise published questions related to this topic.
Want more practice questions?
Practice in App →Opposite Clock Hands Quick Quiz
Attempt 5 questions and check your score instantly.
Keep practising
Practice more Opposite Clock Hands questions in the PrepShots app and continue from your current topic.
Practice More Questions - Start ₹1 Trial →Quick Revision Notes
Opposite Clock Hands Revision Points
Use angular positions and the 11-denominator formula to calculate times at which the clock hands form a straight line.
- Hour-hand angle at H:M = 30H + 0.5M degrees.
- Minute-hand angle at H:M = 6M degrees.
- Opposite hands have an angular separation of 180°.
- For the interval H to H + 1, use M = (60H ± 360)/11 and retain 0 ≤ M < 60.
- Between 3 and 4, the opposite time is 3:49 1/11, approximately 3:49:05.
- The hands are opposite at exactly 6:00.
- There are 11 opposite positions in 12 hours and 22 in 24 hours.
- Convert fractional minutes to seconds by multiplying the fraction by 60.
Opposite Clock Hands FAQs
What is the opposite clock hands formula?
For the time between H and H + 1, use M = (60H ± 360)/11. Select the sign that produces a minute value from 0 through 59.
When are the clock hands opposite between 3 and 4?
M = (60 × 3 + 360)/11 = 540/11 = 49 1/11 minutes. Therefore, the time is 3:49 1/11, or approximately 3:49:05.
When are the clock hands opposite between 9 and 10?
M = (60 × 9 − 360)/11 = 180/11 = 16 4/11 minutes. The time is approximately 9:16:21.
Why is the denominator 11 used in opposite clock hands problems?
The relative speed is 6 − 0.5 = 5.5° per minute, which equals 11/2. Solving the 180° separation equation therefore produces a denominator of 11.
How many times are clock hands opposite in 24 hours?
They are opposite 11 times in 12 hours, so they are opposite 22 times in 24 hours.
Are the clock hands opposite at 6:00?
Yes. At 6:00, the hour hand is at 180° and the minute hand is at 0°, so their separation is exactly 180°.