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The minute hand of a clock crosses the hour hand x minutes past 7 in the evening. Some guests come 20 minutes later. At what time do the guests come?
- a)7:58:11 pm
- b)7:10:27 pm
- c)7:45:15 pm
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The minute hand of a clock crosses the hour hand x minutes past 7 in ...
To solve this problem, we need to understand the movement of the hour and minute hands of a clock.
1. Understanding the movement of the clock hands:
- The hour hand completes one full rotation in 12 hours, or 720 minutes.
- The minute hand completes one full rotation in 60 minutes.
2. The time when the minute hand crosses the hour hand:
- Let's assume the time when the minute hand crosses the hour hand is at T hours and X minutes past T.
- At T hours, the hour hand would have covered (T/12) * 360 degrees.
- At X minutes past T, the minute hand would have covered (X/60) * 360 degrees.
- Since the minute hand crosses the hour hand, the difference between their angles would be either 0 or 180 degrees.
- Therefore, the equation can be written as: (T/12) * 360 - (X/60) * 360 = 0 or (T/12) * 360 - (X/60) * 360 = 180.
3. Solving the equation:
- Let's consider the first equation: (T/12) * 360 - (X/60) * 360 = 0.
- Simplifying this equation, we get: 6T - X = 0.
- We are given that X minutes past 7, so T = 7.
- Substituting the value of T, we get: 6(7) - X = 0.
- Solving this equation, we find X = 42.
4. Finding the time when the guests arrive:
- The guests arrive 20 minutes later, so the time when the guests arrive is 7 hours and 42 + 20 = 62 minutes past 7.
- We need to convert 62 minutes to hours and minutes, which is 1 hour and 2 minutes.
- Adding 1 hour and 2 minutes to 7:00 PM, we get the time when the guests arrive as 8:02 PM.
Therefore, the correct answer is option A) 7:58:11 PM.
1. Understanding the movement of the clock hands:
- The hour hand completes one full rotation in 12 hours, or 720 minutes.
- The minute hand completes one full rotation in 60 minutes.
2. The time when the minute hand crosses the hour hand:
- Let's assume the time when the minute hand crosses the hour hand is at T hours and X minutes past T.
- At T hours, the hour hand would have covered (T/12) * 360 degrees.
- At X minutes past T, the minute hand would have covered (X/60) * 360 degrees.
- Since the minute hand crosses the hour hand, the difference between their angles would be either 0 or 180 degrees.
- Therefore, the equation can be written as: (T/12) * 360 - (X/60) * 360 = 0 or (T/12) * 360 - (X/60) * 360 = 180.
3. Solving the equation:
- Let's consider the first equation: (T/12) * 360 - (X/60) * 360 = 0.
- Simplifying this equation, we get: 6T - X = 0.
- We are given that X minutes past 7, so T = 7.
- Substituting the value of T, we get: 6(7) - X = 0.
- Solving this equation, we find X = 42.
4. Finding the time when the guests arrive:
- The guests arrive 20 minutes later, so the time when the guests arrive is 7 hours and 42 + 20 = 62 minutes past 7.
- We need to convert 62 minutes to hours and minutes, which is 1 hour and 2 minutes.
- Adding 1 hour and 2 minutes to 7:00 PM, we get the time when the guests arrive as 8:02 PM.
Therefore, the correct answer is option A) 7:58:11 PM.
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Community Answer
The minute hand of a clock crosses the hour hand x minutes past 7 in ...
We know that in 60 min, the minute hand gains 55 minutes over the hour hand. At 7 o'clock, the minute hand and the hour hand are 35 min apart. To cross the latter, the min hand must gain 35 min.
Since the min hand gains 55 min in 60 min, therefore
it will gain 35 min in
So, the guests come at 7:58:11 pm.
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The minute hand of a clock crosses the hour hand x minutes past 7 in the evening. Some guests come 20 minutes later. At what time do the guests come?a)7:58:11 pmb)7:10:27 pmc)7:45:15 pmd)None of theseCorrect answer is option 'A'. Can you explain this answer?
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