Test Level 1: Clocks & Calendars - 2 - CAT MCQ

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.

Clearly, Hour hand will point in East direction at 1.30 pm.

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. 

Apply direct formula to calculate the angle:
30 
∴ Required angle = 30 (Take +ve because the hour hand is ahead of the minute hand.)
= 60 + 10 = 70°

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°

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.

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

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.

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 4 o'clock, the angle between the hands is 120 degrees.
At 8:45 p.m, the angle is

55 min spaces are covered in 60 min
60 min. spaces are covered in

Loss in 64 min

Loss in 24 hrs

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

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.

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.

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