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A watch was set right at 7 am. It gains 5 seconds in 3 minutes. In the afternoon of the same day, when the watch indicated 4:15, the true time was
Watch was set right at 7 am.
Time from 7 am to 4.15 pm = 9 hours 15 minutes = 37/7 hours
3 minutes 5 seconds of this clock = 3 minutes of the correct clock
Thus, 37/720 hours of this clock = 1/20 hours of the correct clock
Therefore, 37/4 hours of this clock = hours of the correct clock
= 9 hours of the correct clock
Therefore, 9 hours 15 minutes of this clock = 9 hours of the correct clock
Hence, the correct time is 9 hours after 7 am i.e. 4 pm.
A clock is so placed that at 12 noon, its minute hand points towards Northeast. In which of the following directions does its hour hand point at 1.30 pm?
Clearly, Hour hand will point in East direction at 1.30 pm.
What time will it be 18 hours from now in India, if in USA, it is 4 hours 15 minutes ?
(Given that India is 9 hours 30 minutes ahead of USA)
We know that the time difference between India and USA is 9 hours 30 minutes.
India is 9 hours 30 minutes ahead of USA.
Time in India = 4 hours 15 minutes + 9 hours 30 minutes = 13 hours 45 minutes
Required time after 18 hrs = 13 hours 45 minutes + 18 hrs = 7 hours 45 minutes
Hence, it is 7 hours 45 minutes the next morning.
At what angle are the hands of a clock inclined at 20 minutes past 6 a.m.?
Apply direct formula to calculate the angle:
∴ Required angle = 30 (Take +ve because the hour hand is ahead of the minute hand.)
= 60 + 10 = 70°
At what angle are the hands of a clock inclined at 15 minutes past 5?
Apply direct formula: 30
Thus, required angle = 30 (Take +ve sign because the hour hand is ahead of the minute hand.)
Thus, required time = 60 + 7.5 = 67.5°
Which of the following years has the same calendar as 1700?
Total number of odd days from 1700 to 1705 is remainder (7/7) i.e. 0.
So, after the year 1705, the year i.e 1706 has the same calendar as 1700.
Therefore, option c is the correct answer.
At what time between 5 and 6 are the hands of a clock coincident?
Hands of the clock will be coincident after, minutes past x, where x is the any whole number from 1 to 12.
∴ Between 5 and 6, the hands will be coincident after, 5 × 5 × minutes past 5
Rocky went out between 7 o'clock and 8 o'clock. At 8:30 p.m., he realised that the minute hand of the clock was as much behind the hour hand as the hour hand was behind the minute hand when he had gone out. At what time after he went out did Rocky look at his watch?
At 8:30 p.m., angular distance between hour hand and minute hand is
When Rocky went between 7 to 8 p.m., the angular distance was 75 degrees.
Atminutes past 7 o'clock, angle made by minute hand =
Angle made by hour hand =
Difference = 310.9 - 235.9 = 75°
Hence, option (a) is the correct option.
If the hands of a clock coincide every 66 minutes (true time), how much does the clock gain or lose every hour?
In a correct clock, the minute hand overlaps the hour hand every minutes.
∴ Gain in 66 minutes = - 66 = - 6/11 minutes. Negative gain is a loss.
∴ Loss in 1 hour = minutes = 60/121 minutes
At what time between 4:15 a.m. and 5:05 a.m. will the angle between the hour hand and the minute hand of a clock be the same as the angle between the hands at 8:45 p.m?
At 4 o'clock, the angle between the hands is 120 degrees.
At 8:45 p.m, the angle is
If the hour-hand and the minute-hand of a clock coincide every 64 minutes, how much does the clock gain or lose everyday?
55 min spaces are covered in 60 min
60 min. spaces are covered in
Loss in 64 min
Loss in 24 hrs
At what time will the hands of a clock be together between 3 o'clock and 4 o'clock?
Using direct formula,
where m - minutes and h - hours
Time, between 3 o'clock and 4 o'clock, at which the hands will be together =
minutes past 3 o'clock
A defective watch which gains uniformly, is 5 minutes slow at 8 o'clock in the morning on Sunday and it is 5 minutes 48 seconds fast at 8 pm on following Sunday. When was it correct?
Sunday 8 am to next Sunday 8 pm time duration 24 × 7 + 12 = 180 hrs.
In 180 hrs total gain = 10 min 48 s = 648 s
Gain of 5 min = 300 s will be obtained in
Hence, Sunday 8 am + 83 h 20 min = Wednesday 7 : 20 p.m.
How many times are the hands of a clock at right angles in a day?
Hands will be at right angle twice every hour except from 2 to 4 and 8 to 10 where hands will be at right angle only thrice instead of four times.
Thus, hands will be at right angle 22 times in 12 hours or 44 times in 24 hrs.
At what time between 4 and 5 will the hands of a watch point in the opposite directions?
Hands are pointing in opposite directions. It means hands are 180° apart or they are 30 minutes apart.
Required time = (5x + 30) × 12/11 minutes past x