How much does a watch lose per day , if its hands coincide every 64 min?

At 1 O' clock the the hour hand is at 1 and the minute hand is at 12.
Thus, they are 5 min spaces apart.
To be together, the minute hand must gain 5 min over the hour hand .
55 min are gained by minute hand in 60 min.
5 min will be gained by it in = (60/55 x 5 ) = 60/11 = 5⁵/₁₁ min
Hence, the hands will coincide at 5⁵/₁₁ min past 1 .

If the first Saturday of June is in lst. Then, next Saturday will be on 8th, 15th , 22nd and 29th. So , last Saturday will be on 29th.

In every hour the hand of clock are right angles 2 times, so in a days i.e., 24 h they will be at right angle 48 times.

Pries gave the information to the devotee at 7 :05 am .

The actual time show is 8 h 15 min .

Last two digits of year : 06
Divided by 4 :01
Date: 31 (last day will be 31st Dec)
Month code : 6
Final value : 44
On dividing by 7, we get 2 as remainder. As year is between 2000 - 2099, so 1 has to be subtracted, now the result
= 2 - 1 = 1
1 is the day code for Sunday.

At 5 O' clock, the minute hand is 25 min space apart. The two hands will be 5 min apart between 5 and 5 : 30, if the minute hand is (25 - 5) i.e, 20 min spaces behind the hour hand.
Now, 55 min are gained in 60 min.
20 min are gained in = (60/55 x 20) = (240/11) = 21⁹/₁₁ min
So, the hands will be 5 min apart at 21⁹/₁₁ min past 5.

Total hours from 6 : 14 am morning to evening 6 : 14 pm = 12 h and total hours from 6 : 14 pm evening to 8 : 02 pm evening = 8 : 02 - 6 : 14 = 1 : 48 h i.e., 1 h and 48 min

? Total hours and minutes
= 12 h + 1 h 48 min
= 13 h and 48 min

A leap year must be divisible by 4, as every 4th year is a leap year.

As 2016 is completely divisible by 4.