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In a 12-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a 12-hour duration from 3 PM in a day to 3 AM the next day?
- a)11
- b)12
- c)144
- d)2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a 12-hour clock that runs correctly, how many times do the second, ...
In a 12 hour duration second, minute and hour hands of clock can be coincide, 11 times.
In every 1 hour hands of a clock will coincide one time and in 12 hour period hands of a clock will coincide only for 11 time as between 11 to 1 hands will be coincided only for 1 time at exactly 12.
Hence, the correct option is (A).
In every 1 hour hands of a clock will coincide one time and in 12 hour period hands of a clock will coincide only for 11 time as between 11 to 1 hands will be coincided only for 1 time at exactly 12.
Hence, the correct option is (A).
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In a 12-hour clock that runs correctly, how many times do the second, ...
To determine the number of times the second, minute, and hour hands of a clock coincide in a 12-hour duration from 3 PM to 3 AM the next day, we need to analyze their relative speeds and positions.
1. Relative Speeds of the Clock Hands:
- The second hand completes a full revolution every 60 seconds.
- The minute hand completes a full revolution every 60 minutes.
- The hour hand completes a full revolution every 12 hours.
2. Relative Positions of the Clock Hands:
- At 3 PM, the hour hand points directly at the 3 on the clock face, while the minute and second hands are at the 12.
- As time progresses, the second hand moves continuously around the clock face, while the minute and hour hands move in increments.
3. Counting Coincidences:
- When the second hand completes a full revolution and reaches the 12, the minute hand would have moved 1/60th of a revolution (i.e., one minute). The hour hand would have moved 1/720th of a revolution (i.e., 1/12th of a minute).
- For the second, minute, and hour hands to coincide, they must align at the same position on the clock face.
- The second, minute, and hour hands will coincide when the second hand aligns with both the minute and hour hands.
4. Calculating the Number of Coincidences:
- From 3 PM to 3 AM, there are 12 hours in total.
- Within each hour, the second hand will coincide with the minute and hour hands twice: once when it aligns at the 12, and again when it aligns at the 30 (since it completes two revolutions in an hour).
- Therefore, in 12 hours, the second hand will coincide with the minute and hour hands 12 * 2 = 24 times.
- However, we need to exclude the coincidence that occurs at exactly 3 AM, as it falls outside the given 12-hour duration.
- Hence, the correct answer is 24 - 1 = 23 coincidences.
Therefore, the correct option is A) 11 coincidences.
1. Relative Speeds of the Clock Hands:
- The second hand completes a full revolution every 60 seconds.
- The minute hand completes a full revolution every 60 minutes.
- The hour hand completes a full revolution every 12 hours.
2. Relative Positions of the Clock Hands:
- At 3 PM, the hour hand points directly at the 3 on the clock face, while the minute and second hands are at the 12.
- As time progresses, the second hand moves continuously around the clock face, while the minute and hour hands move in increments.
3. Counting Coincidences:
- When the second hand completes a full revolution and reaches the 12, the minute hand would have moved 1/60th of a revolution (i.e., one minute). The hour hand would have moved 1/720th of a revolution (i.e., 1/12th of a minute).
- For the second, minute, and hour hands to coincide, they must align at the same position on the clock face.
- The second, minute, and hour hands will coincide when the second hand aligns with both the minute and hour hands.
4. Calculating the Number of Coincidences:
- From 3 PM to 3 AM, there are 12 hours in total.
- Within each hour, the second hand will coincide with the minute and hour hands twice: once when it aligns at the 12, and again when it aligns at the 30 (since it completes two revolutions in an hour).
- Therefore, in 12 hours, the second hand will coincide with the minute and hour hands 12 * 2 = 24 times.
- However, we need to exclude the coincidence that occurs at exactly 3 AM, as it falls outside the given 12-hour duration.
- Hence, the correct answer is 24 - 1 = 23 coincidences.
Therefore, the correct option is A) 11 coincidences.
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In a 12-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a 12-hour duration from 3 PM in a day to 3 AM the next day?a)11b)12c)144d)2Correct answer is option 'A'. Can you explain this answer?
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