Problems based on Clocks and calender

CLOCKS.

• Here “#” means degrees.

• Normal clock has 60 divisions and each division =6 #
• In 60 minutes , minute hand moves 60 divisions whereas hour hand covers 5 divisions whereas hour hand covers 5 divisions, therefore minute hand overtakes 55 divisions in 60 minutes, so to overtake 1 division it needs 12/11 minutes.
• Minute hand covers 12 times the no. of divisions covered by hour hand in same time.
• Whenever u need to imagine; imagine the position of hand at exact hour, because u know the gap between the hour hand and minute hand=( hour*5) and minute hand is behind
• Angle between hands – (11m-60h)/2, If the angle calculated does not exists in the ans. options, then subtract your ans. from 360#
• Whatever position comes 1 in an hour, it takes place 11 times in 12 hrs.
• When u get ans. in decimals then remember base is 60.
• For every hour the gap is 60/13
• I f two watches move at different speeds, then they show the same time when the gap is 12hrs. or 720 minutes.
• We use the concept of ratio to find time.
In a normal watch hands coincide every 65 5/11 minutes. If it is written that hands are coinciding every 65 minutes. it means, true time is 65 minutes but watch is giving 65 5/11 minutes, so it is gaining 5/11 minutes every 65 minutes, therefore to calculate the variance , we find the number of time periods of 65 minutes and multiply it by 5/11

Q. when will there be an angle of 30# between 5 and 6?
Method- 5*5= 25
30/6= 5, 6 here means 6 divisions.
Now we get 2 answers-
i. 25-5=20 so 20*(12/11)
ii. 25+5=30 so 30*(12/11)

Q. what time between 5 and 6 in a railway clock both hands will be together.

Q. Between 7 and 8 , what time will the minute hand and the hour hand be pointing towards each other.

Q. Between 5 and 6 both the hour hand and the minute hand are equidistant from 5, but they r not together. What is the time?

Q. what is the change in angle from 3:10 to 3:20 pm.?

A train came at 4:15 and left between 4 and 5 and the angle remained same. What is the duration of the halt?

Q. I sent my servant between 3 and 4 and he came back between 4 and 5. hands had interchanged their positions. What time he came back and went out. How much time had the servant gone out?

Q. A watch looses 3 minutes every 2 hrs, it was set at 8:00 am on Sunday. When will it show the same time again.

Q. A watch gains 0.25% in the 1st week then losses 0.5% in the 2nd week. What variance it shows?

Q. In a wall clock, the minute hand is 6 inches long and hour hand is 4 inches long, what is the difference in area swept by both the hands between 2:15 and 4:15?

Q. At 8:00 am on Sunday watch A was behind by 10 minutes and watch B was ahead by 12 minutes. On Monday at 2:00 pm watch A was ahead by 5 minutes and watch B was behind by 6 minutes.

i. When watch A showed the correct time what was the time in watch A.
ii. When watch B showed the correct time what was the time in watch B.
iii. When did watch A and B show the same time?
iv. When watch A and B showed the same time, what was the time in A and B.

Q. A clock takes 6 sec. to strike 6, how much time it will take to strike 12?



CALENDAR.

1. 1st January 0001 was a Monday.
2. Calendar repeats after every 400 years.
3. Leap year- it is always divisible by 4, but century years are not leap years unless they are divisible by 400.
4. Odd days- remainder obtained when no. of days is divided by 7. Normal year has 1 odd day and leap year has 2 odd days.
5. Calendar moves ahead by number of odd days.
6. While checking leap year just analyze whether February falls in that period or not.
7. Century has 5 odd days and leap century has 6 odd days.
8. Take out net odd days.( add all the odd days and again divide by 7)
9. In a normal year 1st January and 2nd July and 1st October fall on the same day. In a leap year 1st January 1st July and 30th September fall on the same day.
10. 1st January 1901 was Tuesday.
11. We calculate odd days on the basis of the previous month.

Example – what day is it on 29th August 1982?
Method- As we know 1/1/1901 was a Tuesday now we take 1982 and 1901
- 1982-1901=81 years.
- 81/4=20…. ( disregard decimal)
- 81+20=101
- 101/7- remainder is 3, so 3 days from Tuesday is Friday.
-Now check whether it is a leap year or not. In this case it is not a leap year. Therefore 2nd July will be Friday
- Now we have to go month wise . 2nd august = 3odd days= so from Friday 3 odd days will be Monday so 29th August will be a Sunday.