Clocks Questions and Answers

If 10th October is Sunday then 1st October is Friday.
Now, September has 30 days which means it has 2 odd days (30/7)
So, 1st of September will be Wednesday

Now August has 31 days but we need to calculate the 8^th day

So, 31/7 gives 3 odd days

If 1^st August is Sunday then 8^th day of August will be also Sunday.

Now, let's calculate the time difference between when you set the clock right (9:00 AM) and when you returned home (5:20 PM).

Time difference = 5:20 PM - 9:00 AM

First, let's convert both times to 24-hour format for easier calculations.

5:20 PM in 24-hour format = 17:20
9:00 AM in 24-hour format = 9:00

Now, we can calculate the time difference:

Time difference = 17:20 - 9:00

Since we are dealing with time, we need to borrow 1 hour from the hours column:

Time difference = 8:20

Total hours in minutes = 500 minutes
Gain in seconds = (500/4) * 7 = 875
So, Total extra minutes = 14.58 minutes

So, actual time = 5:05 pm (approx).

The clock gains 5 seconds every hour

So in 1 day, i.e. 24 hours it gains 120 seconds

From February 5 to March 2, there are 27 days (as we are counting from 4’o clock to 4’o clock)

= 120*27

=3240 seconds

= 3240/60

= 54 minutes

This means the clock on 2nd March is running 54 minutes ahead of the actual time i.e. 4’o clock. So the current time is 4:54

60 minutes = 30 degrees

1 minute = 30/60 = 0.5 degrees

54 minutes = 54*0.5 = 27 degrees

At 4 the angle made by hour hand and the minute hand = 120 degrees

Therefore at 4:54 = 120+27 = 147 degrees

For a sector, the angle subtended is 30 degrees.

So here are 4 sectors between the hour hand on 8 and minute hand on 20 i.e.
30 x 4 = 120 degrees.

18th July, 1996 = (1995 years + duration between 1.1.1996 to 18.7.1996)

1600 years have 0 odd days

300 years have = (5 x 3) =1

95 years have 23 leap years in total plus 72 normal years.

Odd days in 95 years ( 23 * 2 + 72 *1 (odd day) = 118 = 118/7 gives 6 odd days.

200 days = (28 weeks + 4 odd day)

Total odd days = (0  + 1 +  6 + 4) =  11 days = 1 week and 4 odd days

4th day is Thursday.

At 3:00 the hour needle would be on 3 and the minute hand would be on 12

Which meant there is a 15 minute space between them and to collide the minute needle should advance 15 mins. Above the hour needle.

Therefore 55 minutes will be advanced in 60/55 * 15 = 16 4/11 minutes

Hence the hands will coincide at  16 4/11 past 3

At 4:00 the minute needle will be 20 minutes apart from the hour needle. And to form a right angle, they will be 15 minutes apart

When the min. hand is 15 minute space behind the hour needle, and to come at this position the minute needle has to advance (20-15)= 5 minute space

Now it will take 60 mins. To advance or gain 55 minute space.

Therefore 5 min. space will be advanced in 60/55 *5 = 5 5/11 minutes

Therefore they will be at the right angle at  past 5 5/11 min past 5

At 8:00 hr. needle will be on 8 and the minute needle will be at 12 and both of them will be 20 minutes apart from each other. And to formulate a single straight line without being together the needles must be 30 minutes space away from each other. Hence the minute needle must gain (30-20= 10 Mins.) space above the hour needle.

So in 60 Minutes total 55 minutes are gained.

Hence to gain 10 mins. It will take 60/55*10 - 10 10/11 minutes

Therefore the needles will formulate a straight line without being together at 8 past 10 10/11 minutes

If the clock runs correctly then the minute needle gets advanced by 55 minute over the hour needle in every 60 minutes. And to unite together the minute needle must advance 60 minutes above the hour needle.

Further since 55 minutes are extended in every 60 minutes

Therefore 60 minutes will be advanced in 65/55 *60 = 65 5/11 min.

But as per the question they are together after 65 minutes

Therefore gain in 65 minutes= 65 5/11 - 65 = 5/11

Gain in 24 hrs= 5/11 * (60+24)/65 = 10 10/143 minutes

Time between 8:00 Am on Sunday to 8:00 Pm on the coming Sunday= 7 days and 12 hrs= 180 hours.

Thus a watch gains 5 + 5 4/5 minutes or 54/5 minutes in 180 hrs

Now  54/5  min are gained in 180 hrs

Therefore 5 min. are advanced in 180*5/54 *5= 83 hrs 20 min or 3 days 11 hrs 20 min