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Between 6 PM and 7 PM the minute hand of a clock will be ahead of the hour hand by 3 minutes at 
  • a)
    6: 15 PM  
  • b)
    6: 18 PM  
  • c)
    6: 36 PM  
  • d)
    6: 48 PM 
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Between 6 PM and 7 PM the minute hand of a clock will be ahead of the ...
Solution:

To find out the time when the minute hand of a clock will be ahead of the hour hand by 3 minutes, we need to use the following formula:

Angle traced by hour hand in h hours = 30h degrees
Angle traced by minute hand in m minutes = 6m degrees
Angle between hour hand and minute hand = 30h - 11/2m degrees

Let's assume that the time when the minute hand is ahead of the hour hand by 3 minutes is x. Then we can write:

Angle between hour hand and minute hand = 3 minutes = 6 degrees

Using the above formula, we get:

30h - 11/2m = 6

We know that between 6 PM and 7 PM, the hour hand moves from 180 degrees to 210 degrees, and the minute hand moves from 0 degrees to 360 degrees. Let's substitute these values in the above formula and solve for x:

30h - 11/2m = 6
30(6) - 11/2x = 6
180 - 5.5x = 6
174.5 = 5.5x
x = 31.8

Therefore, the time when the minute hand of a clock will be ahead of the hour hand by 3 minutes is 6:36 PM. Hence, option C is the correct answer.
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Between 6 PM and 7 PM the minute hand of a clock will be ahead of the ...
Option c
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Between 6 PM and 7 PM the minute hand of a clock will be ahead of the hour hand by 3 minutes ata)6: 15 PM b)6: 18 PM c)6: 36 PM d)6: 48 PMCorrect answer is option 'C'. Can you explain this answer?
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