Calendars Clocks

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What is the astronomicalsignificance of 1 year?

Time taken for one revolutionaround the sun

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How many days for one

revolution around thesun?

365 - in an ordinary year

366 - in a leap year

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What is a leap year?

All years divisible by 4Except those by 100, e.g. 1900

Including those by 400 e.g.2000

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The 13th of December 2004 is a Monday. What

will be the day on 13th of December 2005?

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2005 has 365 days

i.e 52 weeks and 1 days

So one year later the day willbe Tuesday

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The definition of an oddday

This additional day is called anodd dayHow many odd days does aleap year have?2

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How many odd days does

a century have?

24 leap years and 76 non-leapyears

24 x 2 + 76 x 1 = 124 odd days

i.e. remainder of 124/7 = 5

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If today is Sunday, whatwill be the day 100 years

from now?100 years later the day will be aFriday

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How many odd days are

there in 200 years?5 odd days in a 100 years.So 10 odd days in 200 years.Odd days can never be greater than 7Odd days = 3

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How many odd days arethere in 300 years?

5 odd days in a 100 years.

3 odd days in 200 yearsSo 1 odd days in 300

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How many odd days arethere in 400 years?

1 odd days in 3005 + 1 odd day in last 100 years

So total = 7 or 0 odd days

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What was the day on the10th of May 1999?

1600 years there will be 0 odddays

300 years after that, there willbe 1 odd day

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98 years, 4 months and 10days

122 odd days, net odd days = 3

4 months and 10 days of 1999,

days elapsed = 130So net odd days = 4

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The Resource Center

Clocks

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The Resource Center

What is the relative speedof the minute hand over

the hour hand?

55 min spaces/ hour

Or 11/12 min spaces/ min

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At what time between 4

and 5 are the minute andhour hand together?

Relative dist of 20 min spaces

Time required = 20 / (11/12) =240 / 11 or 21 9/11 minutes

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Relative Distance of 5 minutes

Time reqd = 5 / ( 11/12) =

5 + 5/11 minutes.

At what time between 4

and 5 are the minute andhour hand be at right

angles?

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Also at relative distance of

35 minutes

Time required for this is35/ ( 11/12) = 38 + 2/11 minutes.

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A clock is set right at 8

AM. The clock gains 10minutes in 24 hours. Whatwill be the true time whenthe clock indicates 1 PM

on the next day?

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Time from 8 am to 1 PM on the

following day is 29 hrs.Now, 24 hrs 10 min of this clock

= 24 hours of correct clock.So 29 hours of this clock is

29*24/2410 = 28 hrs 48 min.So the time is 12 minutesbefore 1 PM.

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A watch gains uniformly. It

was observed that it was5 min slow at 12 oclock in

the night on Sunday. OnThursday at 6 PM it was 5min 48 second fast. When

was it correct?

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The time between 12 Oclockon Sunday night and 6 PM on

Thursday = 90 hours.Now the watch gains 5 + 29 /5= 54/5 minutes in 90 hours.

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So the watch gains 5 minutes in90 x 5 x 5 / 54 = 125 / 3 hours

= 41 hours 40 minutes.Thus, the watch is correct at 5:40 on Monday.

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To conclude

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Odd days in

1 year? 1

100 years? 5200 years? 3400 years? 0

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What is the relative speedof the min hand over the

hour hand?

55 min spaces / hour

Or 11 /12 min spaces / min