Clocks and Calendars
- 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.
- Number of times 29th day of the month occurs in 400 consecutive years is:
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On the basis of above given question , we know that
400 consecutive years contain 97 leap years.
∴ In 400 consecutive years February has 29 days 97 times and the remaining 11 months have 29th day
400 × 11 = 4400 timesCorrect Option: A
On the basis of above given question , we know that
400 consecutive years contain 97 leap years.
∴ In 400 consecutive years February has 29 days 97 times and the remaining 11 months have 29th day
400 × 11 = 4400 times
∴ 29th day of the month occurs ( 4400 + 97 ) = 4497 times.
- How many times do the hands of a clock point towards each other in a day?
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According to question , we know that
The hands of a clock point towards each other 11 times in every 12 hours. (because between 5 and 7, at 6 O’clock only they point towards each other) .Correct Option: D
According to question , we know that
The hands of a clock point towards each other 11 times in every 12 hours. (because between 5 and 7, at 6 O’clock only they point towards each other)
So, in a day the hands point towards each other 22 times.
Hence , correct answer will be 22 times.
- At what time between 4 : 30 and 5 will the hands of a clock be in a straight line?
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As per the given above question , we can see that
At 4 O’clock hands are 20 minutes spaces apart. At time between 4 : 30 and 5 the hands will be in straight line when they point in opposite directions and there is a space of 30 minutes. between them. So, to be in this position minute hand has to gain 30 + 20 = 50 minutes. spaces.Minute hand gains 50 minutes in 60 x 50 = 54 6 minutes. 55 11
Correct Option: C
As per the given above question , we can see that
At 4 O’clock hands are 20 minutes spaces apart. At time between 4 : 30 and 5 the hands will be in straight line when they point in opposite directions and there is a space of 30 minutes. between them. So, to be in this position minute hand has to gain 30 + 20 = 50 minutes. spaces. Minute hand gains 50 minutes in= 60 x 50 = 54 6 minutes. 55 11 ∴ Required time = 54 6 minutes past 4. 11
- How often are the hands of a clock at right angle everyday?
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We know that , In every hour there are two positions in which hands are at right angle.
Each of these positions is repeated 11 times in every 12 hours.
∴ In every 12 hours, hands are at right angles 11 + 11 = 22 timesCorrect Option: B
We know that , In every hour there are two positions in which hands are at right angle.
Each of these positions is repeated 11 times in every 12 hours.
∴ In every 12 hours, hands are at right angles 11 + 11 = 22 times and in a day hands are at right angles 22 + 22 = 44 times.
Hence , required answer will be 44 times.
