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At what time between 9 and 10 o'clock will the hands of a watch be together?

If the hands of the watch are together then they make 0 degree angle .

 

Here m represents minutes 

      h represents hours 

Angle = 11/2 (m) - 30 (h) 

      0 = 11/2 (m) - 30(9) 

       0 = 11/2 (m) - 120

      120 = 11/2 (m) 

     540/11 = m 

       m = 49 1/11

They can be together at 9h 49 1/11 m

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Posted by

Virat

At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?

When the hands of the clock is in opposite directions then they make Angle of  180 degree. 

Angle = 11/2 (m) - 30(h)

   180 = 11/2 (m) - 120

  300  = 11/2 (m)

  600/11 = m 

      m =54 6/11

Therefore the hands were in opposite directions when the hands of clocks at 4h 54 6/11 min 

 

 

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Posted by

Virat

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How many times in a day, are the hands of a clock in straight line but opposite in direction?

12 h = 11 times 

24 h = 22 times

 

 

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Posted by

Virat

 

The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:

 

  • Option 1)

     

    85º

     

  • Option 2)

     

    75º

     

  • Option 3)

     

    60º

     

  • Option 4)

     

    105º

     

  • Option 5)

     

    80º

     

Formula to calculate angle = (11m/2) - 30h

Where, m = minute & h = hour

 

Angle between 8h 30 min = 11/2 (30) - 30 (8)

                                               =  165 -240

                                               =  75 degree 

Options no. 2 is correct answer 

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Posted by

Virat

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At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but not together?

At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but not together?

  • Option 1)

    5 min. past 7    

  • Option 2)

    None of these

  • Option 3)

    5\frac{3}{11}  min. past 7

  • Option 4)

    5\frac{5}{11} min. past 7

  • Option 5)

    5\frac{2}{11}  min. past 7

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Posted by

rishi.raj

 

A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:

 

  • Option 1)

     

    59\frac{7}{12}  min. past 3

     

  • Option 2)

     

    4 p.m.

     

  • Option 3)

     

    58\frac{7}{11} min. past 3

     

  • Option 4)

     

    5 p.m.

     

  • Option 5)

     

    2\frac{3}{121} min. past 3

     

Time difference between 7 AM to 4:15 PM = 9 Hours 15 Minutes or 37/4 hours

3 Minutes & 5 Seconds wrong time = 3 Minutes of actual time

37/12 Minutes wrong time = 3 Minutes of actual time

If we convert it into hours,

37/720 hours = 1/20 hours of actual time
37/4 hours of wrong time = 1/20 x 720/37 x 37/4 => 9 Hours

The Actual-time = 7 AM + 9 hours => 4 PM

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Posted by

rishi.raj

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The minute-hand of a clock overtakes the hour-hand at intervals of 65 minutes of the correct time. How much in a day does the clock gain or lose?

 

  • Option 1)

     

    80\frac{80}{341}\; minutes

     

  • Option 2)

     

    850\frac{90}{311}\; minutes

     

  • Option 3)

     

    None of these

     

  • Option 4)

     

    80\frac{60}{341}\; minutes

     

  • Option 5)

     

    80\frac{70}{341}\; minutes

     

In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes.
To be together again, the minute hand must gain 60 minutes over the hour
hand. 
55 min. are gained in 60 min.
60 min is gained in (60/55) x 60 min =720/11 min.
But, they are together after 65 min.
Gain in 65 min =(720/11)-65 =5/11min.
Gain in 24 hours =(5/11 * (60*24)/65)min =1440/143
The clock gains 1440/143 minutes in 24 hours.

Option 3 is the answer.

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Posted by

rishi.raj

 

The minute-hand of a clock overtakes the hour-hand at intervals of 65 minutes of the correct time. How much in a day does the clock gain or lose?

 

  • Option 1)

     

    \dpi{100} 10\frac{108}{121}\; minutes

     

  • Option 2)

     

    \dpi{100} 11\frac{115}{121}\; minutes

     

  • Option 3)

     

    11\frac{109}{121}\; minutes

     

  • Option 4)

     

    10\frac{104}{121}\; minutes

     

  • Option 5)

     

    None of these

     

For these kinds of problems, there is a direct formula

720/(11 - M) (24 x60/M) = Minutes

Where m = intervals of n minutes of the correct time,

(\frac{720}{11}-65)(\frac{24*60}{65}) => \frac{1440}{143}

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Posted by

rishi.raj

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A watch, which gains uniformly, was observed to be 4 minutes, slow at 6 a.m. on a Monday. On the subsequent Thursday at 7 p.m. it was noticed that the watch was 6 minutes fast. When did watch show the correct time?

 

  • Option 1)

     

    5 p.m. Tuesday

     

  • Option 2)

     

    4 p.m. Tuesday

     

  • Option 3)

     

    None of these

     

  • Option 4)

     

    3 p.m. Tuesday

     

  • Option 5)

     

    6 p.m. Tuesday

     

At 6 AM on Monday, the time is shown by the clock = 5: 56

At 7 PM on Thursday, the time shown by the clock = 7:06

Difference between the times in hours = 24 + 24 + 24 + 13 => 85 hours

In 85 Hours clock covered 10 Minutes.

To show the correct time it has to cover 4 Minutes,

Time is taken to gain 4 minutes = 4 x 85/10 => 34 Hours

The exact time when the clock will show correct time = Monday 6 AM + 34 Hours => Tuesday 4 PM

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Posted by

rishi.raj

 

At what time between 5 and 6 O'clock, will the hands of a clock be at an angle of 62°?

 

  • Option 1)

     

    5 hours  17\frac{2}{11}\; minutes

     

  • Option 2)

     

    5 hours  38\frac{6}{11}\; minutes

     

  • Option 3)

     

    5 hours 16 minutes

     

  • Option 4)

     

    Both (2) and (3)

     

  • Option 5)

     

    None of these

     

We know that In 60 Minutes,

Minute hand covers 360 degrees.

Hour hand covers 30 degrees.

In every 60 Min Minute hand covers 330 degrees more than the hour hand.

330 degree in minutes = 55 Minutes

So, we can conclude that in every 60 Minute Minute hand is 55 Minute ahead.

To be 1 minute ahead, time taken by minute hand = 60/55 = 12/11

Case 1 - When the minute hand is behind

The distance while there will be time 5 'o' clock = 25 minutes or 150 degree

distance to be cover to make 62 degrees = 150-62 => 88 degree or 44/3 min

time taken after 5 = 44/3 x 12/11 => 16 minute

So the exact time when the hands will be together = 3: 16

Case-2 When the minute hand is ahead

The distance while there will be time 5 'o' clock = 25 minutes or 150 degree

distance to be cover to make 62 degrees = 150+62 => 212 degree or 106/3 min

time taken after 5 = 106/3 x 12/11 => 38 (6/11) minute

So the exact time when the hands will be together = 3: 38 (6/11) 

Thus, Option(4) will be the answer.

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Posted by

rishi.raj

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