TCS Clocks and Calendar Quiz-1

4 days = 96 hours
long hand makes 1 round (i.e 2*pi*r) in 1 hour, so 96 rounds in 96 hours
short hand makes 1 round in 12 hours, so 8 rounds in 96 hours
Hence total distance = (96*2*pi*8) + (8*2*pi*7) = 1648*pi

If a month has 31 days, and it starts with sunday, Then Sundays,
Mondays, tuesdays are 5 for that month. If this month starts
with monday, then mondays, tuesdays, and wednesdays
are 5 and remaining days are 4 each. so this month start with Monday.

Hour hand makes 360° in its complete rotation, i.e 12 hrs makes 360° or we can say 12hrs*60minutes=720 minutes makes 360°. So hour hand makes 360°/720minutes=0.5°/minute.

Minutes hand makes 360° in its complete rotation, i.e is 60 minutes makes 360°. So minute hand makes 360°/60minutes= 6°/minutes.

Now According to question,

Hour hand will make total angle from mark 12 in clockwise direction ,
0.5°*(60*5+30)=165°
Minute hand will make angle from mark 12 in clockwise direction,
6°*30=180°
So angle between two hands=180-165=15°

Let us start from Monday 10 am to friday 3.00 pm.....total hours=
4 days 5 hrs.=4*24+5=101 hrs.
so total time loses=101*6 minutes=606 minutes=606/60=10 hrs 6 minutes
so actual time=friday 3.00 pm +10 hrs 06 minutes=staurday 1.06 am.

Now, in most of the places they are giving answers as 4.54 AM, which is incorrect. As the clock loses 6 mins. Thus we have to add the time.

hour hand and minute hand coincide every 65:5 minute, so in 5 hour they will
coincide 4 times

The hour hand covers 2*360 degrees in 24 hours, i.e 1440 minutes.
So, in one minute, it covers 1440/720 = 1/2 degree.
Difference in angular distance travelled by the minute hand
and the hour hand in one minute is thus 6-1/2 = 11/2 degrees.
So, on a full rotation (360ᵒ), any similar event between them
will be repeated every 360/(11/2) = 65 5/11 minutes.

ans- 2/7




in aleap year there are 366 days means 52 weeks and 2days. so already we have
52 fridays. now the rest two days can be
(sun, mon), (mon,tues),(tues, wed), (wed, thrus), (thrus, fri),
(fri, sat), (sat, sun)
so, the probability of 53 fridays= 2/7

11..the hands will be together for once per hour..e.g 9.45,10.50..but between 11 and 12 the coming together will be counted as 1 for both hence in 12 hrs time they will be together for 12-1=11 times

57
after 12 oclock 12:21.......=1
from 1 to 9 it is 1.01, 1.11, 1.21, 1.31, 1.41, 1.51.= 6
similarly 2.02,2.12,.................
6*9=54+1=55
after 10 o clock 10:01, 11:11
Ans: 55+2=57

x is present time
1/4(x)+1/2(24-x)=x
solve it then x = 9:36

The clock loses 1% time during the first week.

In a day there are 24 hours and in a week there are 7 days. Therefore, there are 7 * 24 = 168 hours in a week.

If the clock loses 1% time during the first week, then it will show a time which is 1% of 168 hours less than 12 Noon at the end of the first week = 1.68 hours less.

Subsequently, the clock gains 2% during the next week. The second week has 168 hours and the clock gains 2% time = 2% of 168 hours = 3.36 hours more than the actual time.

As it lost 1.68 hours during the first week and then gained 3.36 hours during the next week, the net result will be a -1.68 + 3.36 = 1.68 hour net gain in time.

So the clock will show a time which is 1.68 hours more than 12 Noon two weeks from the time it was set right.

1.68 hours = 1 hour and 40.8 minutes = 1 hour + 40 minutes + 48 seconds.

i.e. 1 : 40 : 48 P.M.