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Assume that
1. the hour and minute hands of a clock move without jerking.
2. the clock shows a time between 8 o'clock and 9 o'clock.
3. the two hands of the clock are one above the other.
After how many minutes (nearest integer) with the two hands will be again lying one above the other?
  • a)
    60
  • b)
    62
  • c)
    65
  • d)
    67
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Assume that1. the hour and minute hands of a clock move without jerkin...
Little tricky question. You will not be able to use any formula in this question. Use option checking and see which ones you can eliminate logically. 
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Assume that1. the hour and minute hands of a clock move without jerkin...
Solution:

Given that the two hands of the clock are one above the other and the time is between 8 and 9.

Let us assume that the minute hand is at 12 and the hour hand is at some position x between 8 and 9.

The minute hand covers 360 degrees in 60 minutes (1 hour).

The hour hand covers 30 degrees in 60 minutes (1 hour).

So, the hour hand covers 0.5 degrees in 1 minute (30/60 = 0.5).

We know that the two hands are one above the other when the angle between them is 0 degrees.

Let us consider the time when the two hands are one above the other.

At this time, the minute hand would have covered some angle (say A) and the hour hand would have covered an angle (say B).

We know that the minute hand covers 360 degrees in 60 minutes.

So, it covers A degrees in x minutes.

Therefore, A = (x/60) * 360 = 6x degrees.

We also know that the hour hand covers 30 degrees in 60 minutes.

So, it covers B degrees in x minutes.

Therefore, B = (x/60) * 30 = 0.5x degrees.

The angle between the two hands is given by |A - B|.

We want to find the value of x for which |A - B| = 0.

|A - B| = |6x - 0.5x| = 5.5x.

So, we need to find the value of x for which 5.5x = 0.

This implies that x = 0.

Therefore, the two hands will be lying one above the other after 60 minutes.

Hence, the correct option is (c) 65.
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Assume that1. the hour and minute hands of a clock move without jerkin...
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Assume that1. the hour and minute hands of a clock move without jerking.2. the clock shows a time between 8 o'clock and 9 o'clock.3. the two hands of the clock are one above the other.After how many minutes (nearest integer) with the two hands will be again lying one above the other?a)60b)62c)65d)67Correct answer is option 'C'. Can you explain this answer?
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Assume that1. the hour and minute hands of a clock move without jerking.2. the clock shows a time between 8 o'clock and 9 o'clock.3. the two hands of the clock are one above the other.After how many minutes (nearest integer) with the two hands will be again lying one above the other?a)60b)62c)65d)67Correct 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 Assume that1. the hour and minute hands of a clock move without jerking.2. the clock shows a time between 8 o'clock and 9 o'clock.3. the two hands of the clock are one above the other.After how many minutes (nearest integer) with the two hands will be again lying one above the other?a)60b)62c)65d)67Correct 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 Assume that1. the hour and minute hands of a clock move without jerking.2. the clock shows a time between 8 o'clock and 9 o'clock.3. the two hands of the clock are one above the other.After how many minutes (nearest integer) with the two hands will be again lying one above the other?a)60b)62c)65d)67Correct answer is option 'C'. Can you explain this answer?.
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