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The angle made by the minute-hand of a clock in going from 4:45 p.m. to 6:15 p.m. is
- a)540°
- b)470°
- c)360°
- d)220°
Correct answer is option 'A'. Can you explain this answer?
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The angle made by the minute-hand of a clock in going from 4:45 p.m. ...
Solution:
To find the angle made by the minute-hand of the clock, we need to find the difference between the angles made by the minute-hand at 4:45 p.m. and 6:15 p.m.
At 4:45 p.m.
The minute-hand is at 9 on the clock face and has covered 45 minutes of the total 60 minutes.
The angle made by the minute-hand with respect to the 12 on the clock face is given by:
Angle at 4:45 p.m. = (360/60) * 45 = 270°
At 6:15 p.m.
The minute-hand is at 3 on the clock face and has covered 15 minutes of the total 60 minutes.
The angle made by the minute-hand with respect to the 12 on the clock face is given by:
Angle at 6:15 p.m. = (360/60) * 15 = 90°
Difference between the angles at 4:45 p.m. and 6:15 p.m.
= Angle at 6:15 p.m. - Angle at 4:45 p.m.
= 90° - 270°
= -180°
However, we need the acute angle between the two angles. So, we take the absolute value of the difference.
Acute angle between the angles = | -180° | = 180°
Therefore, the angle made by the minute-hand of the clock in going from 4:45 p.m. to 6:15 p.m. is 180°.
Option A is the correct answer.
To find the angle made by the minute-hand of the clock, we need to find the difference between the angles made by the minute-hand at 4:45 p.m. and 6:15 p.m.
At 4:45 p.m.
The minute-hand is at 9 on the clock face and has covered 45 minutes of the total 60 minutes.
The angle made by the minute-hand with respect to the 12 on the clock face is given by:
Angle at 4:45 p.m. = (360/60) * 45 = 270°
At 6:15 p.m.
The minute-hand is at 3 on the clock face and has covered 15 minutes of the total 60 minutes.
The angle made by the minute-hand with respect to the 12 on the clock face is given by:
Angle at 6:15 p.m. = (360/60) * 15 = 90°
Difference between the angles at 4:45 p.m. and 6:15 p.m.
= Angle at 6:15 p.m. - Angle at 4:45 p.m.
= 90° - 270°
= -180°
However, we need the acute angle between the two angles. So, we take the absolute value of the difference.
Acute angle between the angles = | -180° | = 180°
Therefore, the angle made by the minute-hand of the clock in going from 4:45 p.m. to 6:15 p.m. is 180°.
Option A is the correct answer.
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Community Answer
The angle made by the minute-hand of a clock in going from 4:45 p.m. ...
Angle made by a minute-hand in 60 minutes = 360°
Angle made by a minute-hand in 1 minute = 360° / 60 = 6°
4:45 p.m. to 6:15 p.m. is a time period of 90 minutes.
So, angle made by the minute-hand in this time period = 90 × 6° = 540°
Hence, option (1) is correct.
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