The minute hand of a clock overtakes the hour hand at intervals of 70 min of the correct time. How much in a day does the clock gain or loss?

Time from 9 pm in a day to 2 pm on the following day = 29 h.
24 h 10 min of this clock = 24 h of the correct clock
or 145/6 h of this clock = 24 h of the correct clock
29 h of this clock = 24 x (6/145) x 29 h of the correct clock
= 28 h 48 min of correct clock
? The correct time is 28 h 48 min after 9 am. This will be 48 min past 1.

Time from 6 am on a day to 11 pm on 4th day = 89 h
Now, 23 h 44 min of this clock = 24 h of correct clock
89 h of this clock = 24 x (15/356) x 89 h of correct clock = 90 h of correct clock
? Correct time will be 12 o' clock (mid-night).

Given that n = 2 and (n + 1) = 3(n < 6)
The hands will be at the same straight line at
? (5n + 30) x 12/11 min past n.
? (5 x 2 + 30 ) x 12/11 min past 2.
? (10 + 30) x 12/11 min past 2.
? 40 x 12/11 min past 2.
? 480/11 min past 2.

At 9 o'clock, the hour hand is at 9 and the minute hand is at 12. it means that the two hands are 15 min spaces apart .To be in the same straight line (but not together ), they will be 30 min space apart .
? The minute hand will have to gain (30 - 15) = 15 min space over the hour hand .

As we Know, 55 min spaces are gained in 60 min.
? 15 min will be gained in (60/55 x 15) min = 180/11 = 16⁴ /₁₁ min

Hence, the hands will be in the same straight line but not together at 16⁴/ ₁₁ min past 9.

Time from 7 am on a day to 6 am after 3 days is 95 h.
Now , 23 h 45 min of the clock in question = 24 h of correct clock
i..e., 95/4 h of the clock in question = 24 h of correct clock
? 95 h of the clock in question = (24 x 4/95 x 95) h of correct clock = 96 h
So, the correct time is 96 h from 7 am, Monday, ie., 7 am, Friday.

If the minute hand of a clock overtakes the hour hand at interval N min of the correct time, then clock losses or gains by
The required result = [(720/11) - N) ] x [(60 x 24)/N) min
Positive for gain and negative for loss Here, N = 64

required time = [(720/11) - 64) ] x [(60 x 24)/64) min
= 32⁸/₁₁ min

The year 2007 is an ordinary year, so it has 1 odd day.
3rd day of the year 2007 was Wednesday.
? 3rd day of the year 2008 will be one day beyond the Wednesday. Hence, it will be Thursday.

The year 2008 is a leap year, so it has 2 odd days, 3rd day of the year 2008 was Friday.
? 3rd day of the year 2009 will be 2 days beyond the Friday.
Hence, the required answer is Sunday.

5th March, 1999 is Friday.
Then, 5 March 2000 = Friday + 2 = Sunday
(2000 is leap year and it crosses 29th feb 2000, so 2 is taken as odd day}

? 5th March 2000 = Sunday
Then, 9th March 2000 = Thursday.

6th March 2005 = Monday.
Then, 6th March 2004 = Monday - 1 days = Sunday.
(2004 is a leap year but it does not cross 29th February of 2004, so only 1 is taken as odd day).
6th March 2004 = Sunday
7th March 2004 = Monday.