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The hands of two clocks coincide every 60 minutes and 72 minutes respectively. What is the approximate time difference between the two clocks (round to closest minute) after 24 hours as measured by a correct clock?
- a)260 minutes
- b)262 minutes
- c)264 minutes
- d)261 minutes
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The hands of two clocks coincide every 60 minutes and 72 minutes resp...
Solution:
To solve this problem, we need to use the concept of relative speed of the two hands. Let the first clock have hour hand H1 and minute hand M1, and the second clock have hour hand H2 and minute hand M2.
Relative speed of H1 w.r.t. M1 = 1/12 revolutions per minute (since H1 makes one revolution in 12 hours)
Relative speed of H2 w.r.t. M2 = 1/12 * 5/6 = 5/72 revolutions per minute (since H2 makes one revolution in 12 * 5/6 = 10 hours)
Now, consider an arbitrary time t. At this time:
Angle between H1 and M1 = 30H1 + 0.5M1 degrees
Angle between H2 and M2 = 30H2 + 0.5M2 degrees
The hands coincide every 60 minutes and 72 minutes respectively. This means that:
30H1 + 0.5M1 - 30H2 - 0.5M2 = 360 degrees (after 60 minutes)
30H1 + 0.5M1 - 30H2 - 0.5M2 = 360 * 5/6 degrees (after 72 minutes)
Simplifying these equations using the relative speeds, we get:
H1 - H2 = 2/11 (after 60 minutes)
H1 - H2 = 5/44 (after 72 minutes)
Now, we need to find the time difference between the two clocks after 24 hours. Let T be the time difference in minutes. Then:
H1 - H2 = T/12 (since H1 and H2 move at 1/12 revolutions per minute)
Also, since the clocks started together, we have:
H1 - H2 = (2/11) - (5/44) = 3/44
Equating the two expressions for H1 - H2, we get:
T/12 = 3/44
T = (3/44) * 12 * 60 = 260/11 minutes
Rounding off to the nearest minute, we get:
T ≈ 262 minutes
Therefore, the approximate time difference between the two clocks after 24 hours is 262 minutes, which is closest to option B.
To solve this problem, we need to use the concept of relative speed of the two hands. Let the first clock have hour hand H1 and minute hand M1, and the second clock have hour hand H2 and minute hand M2.
Relative speed of H1 w.r.t. M1 = 1/12 revolutions per minute (since H1 makes one revolution in 12 hours)
Relative speed of H2 w.r.t. M2 = 1/12 * 5/6 = 5/72 revolutions per minute (since H2 makes one revolution in 12 * 5/6 = 10 hours)
Now, consider an arbitrary time t. At this time:
Angle between H1 and M1 = 30H1 + 0.5M1 degrees
Angle between H2 and M2 = 30H2 + 0.5M2 degrees
The hands coincide every 60 minutes and 72 minutes respectively. This means that:
30H1 + 0.5M1 - 30H2 - 0.5M2 = 360 degrees (after 60 minutes)
30H1 + 0.5M1 - 30H2 - 0.5M2 = 360 * 5/6 degrees (after 72 minutes)
Simplifying these equations using the relative speeds, we get:
H1 - H2 = 2/11 (after 60 minutes)
H1 - H2 = 5/44 (after 72 minutes)
Now, we need to find the time difference between the two clocks after 24 hours. Let T be the time difference in minutes. Then:
H1 - H2 = T/12 (since H1 and H2 move at 1/12 revolutions per minute)
Also, since the clocks started together, we have:
H1 - H2 = (2/11) - (5/44) = 3/44
Equating the two expressions for H1 - H2, we get:
T/12 = 3/44
T = (3/44) * 12 * 60 = 260/11 minutes
Rounding off to the nearest minute, we get:
T ≈ 262 minutes
Therefore, the approximate time difference between the two clocks after 24 hours is 262 minutes, which is closest to option B.
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Community Answer
The hands of two clocks coincide every 60 minutes and 72 minutes resp...
The hands of a correct clock coincide after every 720/11 minutes.
So, 720/11 minutes of the first clock, equal 60 minutes on a correct clock and 720/11 minutes of the second clock equal 72 minutes on a correct clock.
So, in 1 minute on a correct clock, the difference in times of the two clocks is 720/11*[1/60 - 1/72] = 2/11 minutes.
So, time difference in a day is 2880/11 = 262 minutes
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The hands of two clocks coincide every 60 minutes and 72 minutes respectively. What is the approximate time difference between the two clocks (round to closest minute) after 24 hours as measured by a correct clock?a)260 minutesb)262 minutesc)264 minutesd)261 minutesCorrect answer is option 'B'. Can you explain this answer?
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