Clocks and Calendars
- Number of times the hands of a clock are in a straight line everyday is:
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We know that, any relative position of the hands of a clock is repeated 11 times in every 12 hours.
∴ In every 12 hours, hands coincide 11 times and are opposite to each other 11 times.
∴ In every 12 hours, hands are in a straight line 11 + 11 = 22 times.Correct Option: A
We know that, any relative position of the hands of a clock is repeated 11 times in every 12 hours.
∴ In every 12 hours, hands coincide 11 times and are opposite to each other 11 times.
∴ In every 12 hours, hands are in a straight line 11 + 11 = 22 times.
∴ In every 24 hours hands are in a straight line 44 times.
- At what time between 5 and 6 O’clock are the hands of a clock 3 minutes apart?
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Given that , H = 5 and M = 3.
Putting above the values in given formula , we get
{ ∴ Taking + ve and - ve sign respectively }∴ 12 (5H ± M) = 12 (5 x 5 ± 3) = 31 5 and 24 11 11 11 = 120 = 10 10 11 11
Correct Option: A
Here, H = 5 and M = 3.
Putting above the values in given formula , we get
{ ∴ Taking + ve and - ve sign respectively }∴ 12 (5H ± M) = 12 (5 x 5 ± 3) = 31 5 and 24 11 11 11 = 120 = 10 10 11 11
∴ The hands will be 3 minutes apart at 315/11 minutes past 5 and 24 minutes past 5 O’clock. Hence , option A will be required answer .
- How often between 11 O’clock and 12 O’clock are the hands of a clock in integral number of minutes apart?
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As per the given above question , we can say that
At 11 O’clock, the hour hand is 4 spaces apart from the minute hand. Since there are 60 spaces in one hour, so (60 - 4) times .Correct Option: B
As per the given above question , we can say that
At 11 O’clock, the hour hand is 4 spaces apart from the minute hand. Since there are 60 spaces in one hour, so (60 - 4) times, i.e., 56 times the hands of the clock are an integral number of minutes apart.
Hence , required answer is 56 times .
- At what time between 7 and 8 O’clock will the hands of a clock be at right angle?
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Given that , H = 7
We know that ,The two hands of the clock will be at right angles between H and (H + 1) O’clock at minutes past H O’clock= (5H ± 15) 12 11
{ ∴ Taking + ve and - ve sign respectively , we get }= (5 x 7 ± 15) 12 11 = 21 9 and 54 6 11 11 Correct Option: B
Given that , H = 7
We know that ,The two hands of the clock will be at right angles between H and (H + 1) O’clock at minutes past H O’clock= (5H ± 15) 12 11
{ ∴ Taking + ve and - ve sign respectively , we get }= (5 x 7 ± 15) 12 11
∴ The hands of a clock are at right angle at= 21 9 and 54 6 11 11 21 9 minutes past 7 and, 54 6 minutes past 7 O' clock. 11 11
- The watch which gains uniformly is 2 minutes. slow at noon on Sunday and is 4 minutes. 48 seconds. fast at 2 pm on the following Sunday. The watch was correct at:
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As we know that ,
From Sunday noon to the following Sunday at 2 pm, total time = 7 days + 2 hours = (7 × 24 + 2) hours = 170 hours.In this period watch gains ( 2 + 4 ) minutes 48 seconds = 6 48 minutes = 6 4 minutes 60 5 ∴ Watch gains 6 4 minutes in 170 hours . 5 ∴ Watch gains 2 minutes in 170 x 5 x 2 = 50 hours . 34
Correct Option: A
As we know that ,
From Sunday noon to the following Sunday at 2 pm, total time = 7 days + 2 hours = (7 × 24 + 2) hours = 170 hours.In this period watch gains ( 2 + 4 ) minutes 48 seconds = 6 48 minutes = 6 4 minutes 60 5 ∴ Watch gains 6 4 minutes in 170 hours . 5
i.e., 2 days and 2 hours.∴ Watch gains 2 minutes in 170 x 5 x 2 = ( 2 x 24 + 2 ) hours = 50 hours . 34
∴ Watch will be correct at 2 pm on Tuesday.
