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At what time between 2 and 3 O’ clock the hands of clock will make an angle of 1600 ?
- a)20 minutes past 2
- b)30 minutes past 2
- c)40 minutes past 2
- d)50 minutes past 2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
At what time between 2 and 3 O’ clock the hands of clock will ma...
Understanding Clock Angles
To determine the angle between the hands of a clock, we can use the formula:
- Angle = |(30*Hour - (11/2)*Minutes)|
Here, "Hour" is the hour hand position, and "Minutes" is the minute hand position.
Calculating the Positions
1. Hour Hand Position:
- At 2:00, the hour hand is at 60 degrees (2 hours * 30 degrees/hour).
- For every minute, the hour hand moves 0.5 degrees (30 degrees/60 minutes).
- So, if 'm' is the number of minutes past 2:00, the hour hand's position is:
Hour Position = 60 + 0.5m
2. Minute Hand Position:
- The minute hand moves 6 degrees per minute (360 degrees/60 minutes).
- Therefore, the minute hand's position is:
Minute Position = 6m
Setting Up the Equation
We want the angle between the two hands to be 160 degrees. Thus, we set up the equation:
- |(60 + 0.5m) - (6m)| = 160
This simplifies to two cases:
1. Case 1:
60 + 0.5m - 6m = 160
- This leads to:
- -5.5m = 100
- m = -100/5.5 (not applicable)
2. Case 2:
60 + 0.5m - 6m = -160
- This simplifies to:
- -5.5m = -220
- m = 220/5.5 = 40
Conclusion
Therefore, the hands of the clock will make an angle of 160 degrees at 40 minutes past 2. Hence, the correct answer is option 'C' - 40 minutes past 2.
To determine the angle between the hands of a clock, we can use the formula:
- Angle = |(30*Hour - (11/2)*Minutes)|
Here, "Hour" is the hour hand position, and "Minutes" is the minute hand position.
Calculating the Positions
1. Hour Hand Position:
- At 2:00, the hour hand is at 60 degrees (2 hours * 30 degrees/hour).
- For every minute, the hour hand moves 0.5 degrees (30 degrees/60 minutes).
- So, if 'm' is the number of minutes past 2:00, the hour hand's position is:
Hour Position = 60 + 0.5m
2. Minute Hand Position:
- The minute hand moves 6 degrees per minute (360 degrees/60 minutes).
- Therefore, the minute hand's position is:
Minute Position = 6m
Setting Up the Equation
We want the angle between the two hands to be 160 degrees. Thus, we set up the equation:
- |(60 + 0.5m) - (6m)| = 160
This simplifies to two cases:
1. Case 1:
60 + 0.5m - 6m = 160
- This leads to:
- -5.5m = 100
- m = -100/5.5 (not applicable)
2. Case 2:
60 + 0.5m - 6m = -160
- This simplifies to:
- -5.5m = -220
- m = 220/5.5 = 40
Conclusion
Therefore, the hands of the clock will make an angle of 160 degrees at 40 minutes past 2. Hence, the correct answer is option 'C' - 40 minutes past 2.
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At what time between 2 and 3 O’ clock the hands of clock will make an angle of 1600 ?a)20 minutes past 2b)30 minutes past 2c)40 minutes past 2d)50 minutes past 2Correct answer is option 'C'. Can you explain this answer? for CUET Commerce 2025 is part of CUET Commerce preparation. The Question and answers have been prepared according to the CUET Commerce exam syllabus. Information about At what time between 2 and 3 O’ clock the hands of clock will make an angle of 1600 ?a)20 minutes past 2b)30 minutes past 2c)40 minutes past 2d)50 minutes past 2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CUET Commerce 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what time between 2 and 3 O’ clock the hands of clock will make an angle of 1600 ?a)20 minutes past 2b)30 minutes past 2c)40 minutes past 2d)50 minutes past 2Correct answer is option 'C'. Can you explain this answer?.
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