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If the angle between the hour and the minute hand changes from 0 to 20 degrees, then the sum of the angles covered by both the hands at first such incidence would be?
- a)19+(7/11) degrees
- b)21+(7/11) degrees
- c)23+(7/11) degrees
- d)25+(7/11) degrees
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the angle between the hour and the minute hand changes from 0 to 20...
Method I:
Suppose it is 12 o’clock. Now if the hour hand moves x degrees then the minute hand will move (x+20) degrees to create an angle of 20 degrees with the hour hand.
Now, Since 1/2degree is covered by hour hand in 1 minute.
So, 1 degree is covered by hour hand in 1/(1/2)= 2 minutes.
So, x degrees are covered by hour hand in 2x minutes.
Again, Since 6 degrees are covered by minute hand in 1 minute.
So, 1 degree is covered by minute hand in 1/6 minutes.
So, x+20 degrees are covered by the minute hand in (x+20)/6 minutes.
Since the time is same for both the hands to attain the required situation,
so, 2x = (x+20)/6 ⇒ 12x = x+20
⇒ 11x = 20
∴ x = 20/11.
Now, the total angle covered by both the hands = (2x + 20) degrees = 2×20/11 + 20 = 40/11 + 20 = 3×7/11 + 20 = 23×7/11 degrees.
Suppose it is 12 o’clock. Now if the hour hand moves x degrees then the minute hand will move (x+20) degrees to create an angle of 20 degrees with the hour hand.
Now, Since 1/2degree is covered by hour hand in 1 minute.
So, 1 degree is covered by hour hand in 1/(1/2)= 2 minutes.
So, x degrees are covered by hour hand in 2x minutes.
Again, Since 6 degrees are covered by minute hand in 1 minute.
So, 1 degree is covered by minute hand in 1/6 minutes.
So, x+20 degrees are covered by the minute hand in (x+20)/6 minutes.
Since the time is same for both the hands to attain the required situation,
so, 2x = (x+20)/6 ⇒ 12x = x+20
⇒ 11x = 20
∴ x = 20/11.
Now, the total angle covered by both the hands = (2x + 20) degrees = 2×20/11 + 20 = 40/11 + 20 = 3×7/11 + 20 = 23×7/11 degrees.
Method II: Time taken by the two hands to increase the angle between them from 0 to 20 degrees = 20/5.5 = 40/11 minutes.
Sum of the angles covered by hour and minute hands in this time = (6 + 0.5) × (40/11) = (13/2) × (40/11) = 260/11 = 23×7/11 degrees.
Sum of the angles covered by hour and minute hands in this time = (6 + 0.5) × (40/11) = (13/2) × (40/11) = 260/11 = 23×7/11 degrees.
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If the angle between the hour and the minute hand changes from 0 to 20 degrees, then the sum of the angles covered by both the hands at first such incidence would be?a)19+(7/11) degreesb)21+(7/11) degreesc)23+(7/11) degreesd)25+(7/11) degreesCorrect answer is option 'C'. Can you explain this answer?
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If the angle between the hour and the minute hand changes from 0 to 20 degrees, then the sum of the angles covered by both the hands at first such incidence would be?a)19+(7/11) degreesb)21+(7/11) degreesc)23+(7/11) degreesd)25+(7/11) degreesCorrect answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the angle between the hour and the minute hand changes from 0 to 20 degrees, then the sum of the angles covered by both the hands at first such incidence would be?a)19+(7/11) degreesb)21+(7/11) degreesc)23+(7/11) degreesd)25+(7/11) degreesCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the angle between the hour and the minute hand changes from 0 to 20 degrees, then the sum of the angles covered by both the hands at first such incidence would be?a)19+(7/11) degreesb)21+(7/11) degreesc)23+(7/11) degreesd)25+(7/11) degreesCorrect answer is option 'C'. Can you explain this answer?.
If the angle between the hour and the minute hand changes from 0 to 20 degrees, then the sum of the angles covered by both the hands at first such incidence would be?a)19+(7/11) degreesb)21+(7/11) degreesc)23+(7/11) degreesd)25+(7/11) degreesCorrect answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the angle between the hour and the minute hand changes from 0 to 20 degrees, then the sum of the angles covered by both the hands at first such incidence would be?a)19+(7/11) degreesb)21+(7/11) degreesc)23+(7/11) degreesd)25+(7/11) degreesCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the angle between the hour and the minute hand changes from 0 to 20 degrees, then the sum of the angles covered by both the hands at first such incidence would be?a)19+(7/11) degreesb)21+(7/11) degreesc)23+(7/11) degreesd)25+(7/11) degreesCorrect answer is option 'C'. Can you explain this answer?.
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