The number of times in a day the hour hand and the minute hand of a clock are at right angles, is?

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

The actual time show is 8 h 15 min .

2 h 20 min = 140 min
In every hour the minute hand move over 360°.
So, in every minute it will move 360°/60° = 6°
So, in 140 min the minute hand will move over = 6 x 140° = 840°

Angle traced by hour hand in 12 h = 360°
Angle traced by hour hand in 5 h = (360/12) x 5° = 150°

The century year which is completely divisible by 400, is a leap year. Thus, the year 2800 is a leap year.

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.

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 .

Normally, hands of a watch coincide after 65⁵/₁₁ min.
So, loss per hour = 1⁵/₁₁ min
? Loss per day = 24 x 1⁵/₁₁ = 24 x 16/11
= 34¹⁰/₁₁ 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.