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A person goes to a market between 4 p.m. and 5 p.m. When he comes back he finds that the hour hand and the minute hand of the clock have interchanged their positions. For how much time (approximately) was he out of his house?
- a)55.38 minutes
- b)55.48 minutes
- c)55.57 minutes
- d)55.67 minutes
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A person goes to a market between 4 p.m. and 5 p.m. When he comes back...
Let OA be position of the hour hand and OB be the position of the minute hand initially
If they get reversed hour hand has to transverse an angle of θ and minute hand had to traverse an angle of 360 – θ
Let the time taken be ‘t’ minutes
Angle swept by hour hand in 1 minute = 360/ (12 × 60) = 0.5° [∵ It sweeps 360° in 12 hours]
Angle swept by minute hand in 1 minute = 360/60 = 6°
⇒ θ = 0.5t
⇒ 360 – θ = 6t
⇒ 360 – 0.5t = 6t
⇒ 6.5t = 360
∴ t = 360/6.5 ≈ 55.38 minutes
⇒ θ = 0.5t
⇒ 360 – θ = 6t
⇒ 360 – 0.5t = 6t
⇒ 6.5t = 360
∴ t = 360/6.5 ≈ 55.38 minutes
Most Upvoted Answer
A person goes to a market between 4 p.m. and 5 p.m. When he comes back...
Problem Analysis:
Let's assume that the person goes to the market at time T1 and returns back at time T2. We need to find the difference between T2 and T1.
Solution:
To solve this problem, we can use the following steps:
Step 1: Convert the clock positions to angles
The minute hand moves 360 degrees in 60 minutes, so it moves 6 degrees per minute. The hour hand moves 360 degrees in 12 hours, so it moves 0.5 degrees per minute.
Step 2: Calculate the initial positions of the hour and minute hands
At 4 p.m., the hour hand is at the 4-hour mark, which is 120 degrees. The minute hand is at the 12-minute mark, which is 72 degrees.
Step 3: Calculate the final positions of the hour and minute hands
When the hour and minute hands interchange their positions, the minute hand will be at 120 degrees and the hour hand will be at 72 degrees.
Step 4: Calculate the time difference
To find the time difference, we need to calculate how long it takes for the hour and minute hands to move from their initial positions to their final positions. Since the minute hand moves 6 degrees per minute and the hour hand moves 0.5 degrees per minute, we can calculate the time difference by dividing the angle difference (120 - 72 = 48 degrees) by the relative speed (6 - 0.5 = 5.5 degrees per minute).
Step 5: Convert the time difference to minutes
To convert the time difference to minutes, we divide the angle difference by the relative speed: 48 degrees / 5.5 degrees per minute = 8.73 minutes.
Step 6: Convert the minutes to hours and minutes
Since the time difference is less than 60 minutes, we can express it as 0 hours and 8.73 minutes.
Step 7: Add the time difference to the initial time
To find the final time, we add the time difference to the initial time: T2 = T1 + 0 hours 8.73 minutes.
Step 8: Convert the final time to the 12-hour format
To convert the final time to the 12-hour format, we need to check if the hours are greater than 12. If they are, we subtract 12 from the hours and append "p.m." to the time.
In this case, the initial time is 4 p.m., so the final time is 4 + 0 hours 8.73 minutes = 4 hours 8.73 minutes. Since the hours are not greater than 12, the final time is 4 hours 8.73 minutes a.m.
Therefore, the person was out of his house for approximately 8.73 minutes, which is equivalent to 8 minutes and 44 seconds. The correct answer is option A) 55.38 minutes.
Let's assume that the person goes to the market at time T1 and returns back at time T2. We need to find the difference between T2 and T1.
Solution:
To solve this problem, we can use the following steps:
Step 1: Convert the clock positions to angles
The minute hand moves 360 degrees in 60 minutes, so it moves 6 degrees per minute. The hour hand moves 360 degrees in 12 hours, so it moves 0.5 degrees per minute.
Step 2: Calculate the initial positions of the hour and minute hands
At 4 p.m., the hour hand is at the 4-hour mark, which is 120 degrees. The minute hand is at the 12-minute mark, which is 72 degrees.
Step 3: Calculate the final positions of the hour and minute hands
When the hour and minute hands interchange their positions, the minute hand will be at 120 degrees and the hour hand will be at 72 degrees.
Step 4: Calculate the time difference
To find the time difference, we need to calculate how long it takes for the hour and minute hands to move from their initial positions to their final positions. Since the minute hand moves 6 degrees per minute and the hour hand moves 0.5 degrees per minute, we can calculate the time difference by dividing the angle difference (120 - 72 = 48 degrees) by the relative speed (6 - 0.5 = 5.5 degrees per minute).
Step 5: Convert the time difference to minutes
To convert the time difference to minutes, we divide the angle difference by the relative speed: 48 degrees / 5.5 degrees per minute = 8.73 minutes.
Step 6: Convert the minutes to hours and minutes
Since the time difference is less than 60 minutes, we can express it as 0 hours and 8.73 minutes.
Step 7: Add the time difference to the initial time
To find the final time, we add the time difference to the initial time: T2 = T1 + 0 hours 8.73 minutes.
Step 8: Convert the final time to the 12-hour format
To convert the final time to the 12-hour format, we need to check if the hours are greater than 12. If they are, we subtract 12 from the hours and append "p.m." to the time.
In this case, the initial time is 4 p.m., so the final time is 4 + 0 hours 8.73 minutes = 4 hours 8.73 minutes. Since the hours are not greater than 12, the final time is 4 hours 8.73 minutes a.m.
Therefore, the person was out of his house for approximately 8.73 minutes, which is equivalent to 8 minutes and 44 seconds. The correct answer is option A) 55.38 minutes.
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A person goes to a market between 4 p.m. and 5 p.m. When he comes back he finds that the hour hand and the minute hand of the clock have interchanged their positions. For how much time (approximately) was he out of his house?a)55.38 minutesb)55.48 minutesc)55.57 minutesd)55.67 minutesCorrect answer is option 'A'. Can you explain this answer?
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