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A clock is placed at 12 noon its minute hand points towards north east.In which direction does its hour hand point at 1.30pm?
- a)North
- b)East
- c)South
- d)West
- e)Cannot be determined
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A clock is placed at 12 noon its minute hand points towards north east...
Solution:
In order to solve this question, we need to understand the position of the hour and minute hands of a clock at different times.
Position of the Hour Hand:
- The hour hand moves 30 degrees in one hour.
- It completes one full rotation (360 degrees) in 12 hours.
- At 12 noon, the hour hand is pointing towards the south.
Position of the Minute Hand:
- The minute hand moves 6 degrees in one minute.
- It completes one full rotation (360 degrees) in 60 minutes.
- At 12 noon, the minute hand is pointing towards the north-east.
Now, we need to find the position of the hour hand at 1:30 pm.
Angle between the Hour and Minute Hand:
- In general, the angle between the hour and minute hand can be calculated using the formula:
Angle = 0.5 * [(60 * Hour) - (11 * Minutes)]
where Hour is the hour hand position and Minutes is the minute hand position.
Using this formula, we can find the angle between the hour and minute hand at 1:30 pm:
Angle = 0.5 * [(60 * 1) - (11 * 30)]
Angle = 0.5 * (60 - 330)
Angle = 0.5 * (-270)
Angle = -135 degrees
Since the angle is negative, we need to add 360 degrees to it to get the actual angle:
Angle = -135 + 360
Angle = 225 degrees
Direction of the Hour Hand:
- From the position of the angle, we can determine the direction of the hour hand.
- At 225 degrees, the hour hand is pointing towards the east.
Therefore, the correct answer is option B - East.
In order to solve this question, we need to understand the position of the hour and minute hands of a clock at different times.
Position of the Hour Hand:
- The hour hand moves 30 degrees in one hour.
- It completes one full rotation (360 degrees) in 12 hours.
- At 12 noon, the hour hand is pointing towards the south.
Position of the Minute Hand:
- The minute hand moves 6 degrees in one minute.
- It completes one full rotation (360 degrees) in 60 minutes.
- At 12 noon, the minute hand is pointing towards the north-east.
Now, we need to find the position of the hour hand at 1:30 pm.
Angle between the Hour and Minute Hand:
- In general, the angle between the hour and minute hand can be calculated using the formula:
Angle = 0.5 * [(60 * Hour) - (11 * Minutes)]
where Hour is the hour hand position and Minutes is the minute hand position.
Using this formula, we can find the angle between the hour and minute hand at 1:30 pm:
Angle = 0.5 * [(60 * 1) - (11 * 30)]
Angle = 0.5 * (60 - 330)
Angle = 0.5 * (-270)
Angle = -135 degrees
Since the angle is negative, we need to add 360 degrees to it to get the actual angle:
Angle = -135 + 360
Angle = 225 degrees
Direction of the Hour Hand:
- From the position of the angle, we can determine the direction of the hour hand.
- At 225 degrees, the hour hand is pointing towards the east.
Therefore, the correct answer is option B - East.
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A clock is placed at 12 noon its minute hand points towards north east.In which direction does its hour hand point at 1.30pm?a)Northb)Eastc)Southd)Weste)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?
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