Clocks

As, the hour hand covers 360 degrees in 12 hrs. In the clock the time is 3.25 = 3 hrs 25 min = 41/12 hrs. So, the angle traced by hour hand = (360/12 x 41/12) degrees = 205 degrees. The minute hand covers 360 degrees in 60 minutes. So, the angle is traced by minute hand in 25 min = (360/60 x 25) degrees = 150 degrees. Hence, the required angle of the clock = (150- 205/2) degrees = 95/2 degrees.

The given time from 8:00 am on Sunday to 8 pm on following Sunday = 7 days 12 hrs = 180 hrs. So, the clock gains = (5 + 29/5)min = 54/5 min in 180 hrs. Hence, 5 min are gained in (180 x 5/54 x 5)hrs = 83 hrs 20 min = 3 days 11 hrs 20 min. The clock is correct 3 days 11 hrs 20 min after 8 am of Sunday. So, the correct time and day will be 20 min past 7 pm on Wednesday.

From the given information the time from 5 am on a day to 10 pm on the 4th day is 89 hrs. So, 23 hrs 44 min of this clock = 24 hrs of correct clock. Hence, 356/15 hrs of this clock = 24 hrs of correct clock. 89 hrs of the clock = (24 x 15/356 x 89)hrs of correct clock = 90 hrs of correct clock. Hence, the original time will be 11 pm.

From 8 am on a day to 1 pm on the following day will be 29 hrs. So, the clock gains 10 min in 24 hours = 24 hrs of the correct time. Hence, 145/6 hrs of the clock = 24 hrs of the correct clock. 29 hrs of the clock = (24 x 6/145 x 24)hrs of the correct clock = 28 hrs 48 min of the correct clock. The correct time = 28 hrs 48 min after 8 am. Hence, the original time is 48 minutes past 12.

The hour hand covers the angle 360 degrees in 12 hrs. So, the angle is covered by it in 11/3 hrs = (360/2 x 11/3) degrees = 110 degrees . The minute hand covers the angle in 360 degrees in 60 min. So, the angle is covered by it in 40 min = (360/60 x 40) degrees = 240 degrees . Hence, the required angle made by both hands = (240 - 110) degrees = 130 degrees .

For 6 hrs duration hrs hand covered 6 hrs out of 12 hrs
When hrs hand covers 12 hrs it rotates for 360 degree
----------------------------6 --------------------- = (360/12)*6 = 180 degrees

For 6 hrs duration hrs hand covered 6 hrs out of 12 hrs When hrs hand covers 12 hrs it rotates for 360 degree ----------------------------6 --------------------- = 360/12)*6 = 180 degrees

For 6 hrs duration hrs hand covered 12 hrs out of 12 hrs When hrs hand covers 12 hrs it rotates for 360 degree ----------------------------12 --------------------- =(360/12)*12 = 360 degrees

When hrs hand rotates for 360 degree it covers 12 hrs --------------------------------- 180 --------------------- 6 hrs So the time will be: 10:00 AM + 6 hrs = 4:00 PM

When hrs hand rotates for 360 degree it covers 12 hrs --------------------------------- 360 --------------------- 12 hrs So the time will be: 06:00 AM + 12 hrs = 06:00 PM