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At what time between 4 and 5 will the minute hand of a clock be 13 minutes behind the hour hand?
- a)7(7/11) minutes past 4
- b)8(9/11) minutes past 4
- c)9(5/11) minutes past 4
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
At what time between 4 and 5 will the minute hand of a clock be 13 mi...
Solution:
To find the time between 4 and 5 when the minute hand is 13 minutes behind the hour hand, we need to use the following formula:
(11/2) × (M – H) = 13M/60
Where M is the number of minutes past the hour and H is the number of hours past 12.
Let's assume that the minute hand is x minutes past 4, then the hour hand is at 4 + x/60 hours past 12. We can substitute these values in the above formula as follows:
(11/2) × (x/60 – (4 + x/60 – 12)) = 13x/60
Simplifying this equation, we get:
11x/120 – 22 = 13x/60
Multiplying both sides by 120, we get:
11x – 2640 = 26x
Solving for x, we get:
x = 120/15 = 8
Therefore, the minute hand is 8 minutes past 4 when it is 13 minutes behind the hour hand.
Therefore, the correct answer is option B: 8(9/11) minutes past 4.
To find the time between 4 and 5 when the minute hand is 13 minutes behind the hour hand, we need to use the following formula:
(11/2) × (M – H) = 13M/60
Where M is the number of minutes past the hour and H is the number of hours past 12.
Let's assume that the minute hand is x minutes past 4, then the hour hand is at 4 + x/60 hours past 12. We can substitute these values in the above formula as follows:
(11/2) × (x/60 – (4 + x/60 – 12)) = 13x/60
Simplifying this equation, we get:
11x/120 – 22 = 13x/60
Multiplying both sides by 120, we get:
11x – 2640 = 26x
Solving for x, we get:
x = 120/15 = 8
Therefore, the minute hand is 8 minutes past 4 when it is 13 minutes behind the hour hand.
Therefore, the correct answer is option B: 8(9/11) minutes past 4.
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Community Answer
At what time between 4 and 5 will the minute hand of a clock be 13 mi...
At 4 o'clock, the angle is 120°.
In 13 minutes, the difference in angle is:
New angle is 
Angle of 110/2 is covered in 1 minute.
Therefore, angle of 970/2 is covered in:
Therefore, the exact time is 8(9/11) minutes past 4.
Thus, option (2) is correct.
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